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School: UConn
Course: Actuarial Models
MATH 3634 - Actuarial Models Spring 2013 - Valdez Homework 1 Total marks: 100 due Friday, 22 February 2013, 6:00 PM Please write your name and student number at the spaces provided: Name: Student ID: Follow these instructions: There are ve (5) questions
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Final Report Actuarial Staffing Report Contents: Introduction.2 Salary. 2 Benefits.4 Exam Costs. 5 Exam Raises.7 Hiring/Replacing.9 Conclusion. 13 Mr. CFO, I have put together a well-developed and clearly articulated report on the companys lo
School: UConn
1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12), 1922, and 25. For brevity, the symbols R1, R2, stand for row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 2 x1 7 x2 = 5 1
School: UConn
Course: Elem Differential Equations
1. (10 points) Solve the initial Value problem %=yt+%, y(l)=3 iswt) 0') i g 5 41% ;S[cfw_+t)obt (2') KH!:?+aw|+a, gly 5=hf U) h:sef% i) (a) l D d 2. (15 points) Consider the differential equation dE; = where is given by the following graph (a) Sketch th
School: UConn
Course: Calculus I
5/14/2015 TentativeOutlineforMath1131201314 TentativeOutlineforMath1131Fall2013 (Calculus,EarlyTranscendentals,byJamesStewart7thEdition) Week Date Section 1 2 3 Topic FourWaystoRepresentaFunction, andMathematicalModels NewFunctionsfromOldFunctions, 1.3,1.
School: UConn
Course: Financial Mathematics II
Math 3650 Chapter 24 Lecture notes Lets talk about bonds! Corporate Bonds are loans made by corporations to borrow money for investments and growth. Youve all had Math 2620 which teaches you how to price bonds (although Im going to complicate that as we g
School: UConn
Course: Actuarial Statistics
Math 3621 Project Details (similar to the model provided by Prof. Frees in his book and on his website) Overall Your report must be no more than 15 pages long (including all figures, tables, and appendices, 11 point font, spacing of at least 1.15, and 1 m
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 8: Autocorrelations and Autoregressive Models Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut March 31 & April 2, 2015 In this class, we will discuss the following topics Autocorrelations Aut
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 5: Variable Selection Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut Mar 3 and 5, 2015 In this chapter, we will discuss the following topics Automatic variable selection Residual analysis In
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 6: Interpreting Regression Results Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut Mar 10 and 12, 2015 In this class, we will discuss the following topic Interpretations of regression results
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Initial Assessment Essay Risk is everywhere in the world today. With risk comes uncertainty. Not knowing what the future holds can be very daunting, especially in the business world. However, this is where actuaries excel. Actuaries are exper
School: UConn
Course: Actuarial Mathematics I
Math 3630 Life Contingencies I Chapter 6: Premiums Premiums Premiums are the amounts paid to the insurer in exchange for the benets provided to the insured. The premium may consist of one or more payments. In traditional life insurance contracts, the prem
School: UConn
Course: Actuarial Mathematics I
Math 3630 Life Contingencies I Chapter 4: Life insurance Review of (actuarial) interest theory notation We use i to denote an annual eective rate of interest. The one year present value (discount) factor is denoted by v = 1/(1 + i). i (m) is an annual nom
School: UConn
Course: Actuarial Mathematics I
Math 3630 Life Contingencies I Chapter 5: Life annuities Life annuities Here were going to consider the valuation of life annuities. A life annuity is regularly (e.g., continuously, annually, monthly, etc.) spaced series of payments, which are usually bas
School: UConn
Course: Actuarial Mathematics I
Chapter 1: Introduction Math 3630: Life Contingencies Brian M. Hartman, PhD ASA Overview Chapter 1 in the text gives a broad introduction to life insurance. Overview of the industry Definitions History Background Premium: Amount paid by the policy ho
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 7 Asset-Liability Management, Duration, and Immunization Duration (or Macaulay Duration) D or MacD The duration of a stream of payments is a weighted average of the number
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 6 - TERM STRUCTURE OF INTEREST RATES Spot Rate (sn) the level annual interest rate that applies to a currently-issued n-year zero-coupon bond Yield Curve spot rates for zer
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Final Report Actuarial Staffing Report Contents: Introduction.2 Salary. 2 Benefits.4 Exam Costs. 5 Exam Raises.7 Hiring/Replacing.9 Conclusion. 13 Mr. CFO, I have put together a well-developed and clearly articulated report on the companys lo
School: UConn
Course: Elem Differential Equations
1. (10 points) Solve the initial Value problem %=yt+%, y(l)=3 iswt) 0') i g 5 41% ;S[cfw_+t)obt (2') KH!:?+aw|+a, gly 5=hf U) h:sef% i) (a) l D d 2. (15 points) Consider the differential equation dE; = where is given by the following graph (a) Sketch th
School: UConn
Course: Actuarial Models
MATH 3634 - Actuarial Models Spring 2013 - Valdez Homework 1 Total marks: 100 due Friday, 22 February 2013, 6:00 PM Please write your name and student number at the spaces provided: Name: Student ID: Follow these instructions: There are ve (5) questions
School: UConn
Course: Calculus I
Worksheet 4: Derivatives Name: Section No: In the problems below, the parameters a, b, and c are constants. Use implicit dierentiation to dierentiate y with respect to x. (1) x2 y axy 2 = x + y (2) exy = x2 + y 2 (3) sin(x + y) = x + cos(3y) Use logarithm
School: UConn
Course: Calculus I
Worksheet on Limits Name: Discussion Section Number: 1. Tangent and velocity (2.1) The displacement (in meters) of an object moving in a straight line is given by 1 s = 1 + 2t + t2 , 4 where t is measured in seconds. (1) Find the average velocity over eac
School: UConn
Course: Calculus I
Worksheet 6: Integration Name: Section No: (1) Find the most general antiderivative of the function (use C as any constant). (a) f (x) = 1 3 2 4 3 + x x 2 4 5 t4 + 3 t (b) f (t) = t2 (c) g() = cos 5 sin (2) Find f (x) satisfying the given conditions. (a)
School: UConn
Course: Calculus I
Algebra Worksheet Name: Section No: 1. Simplifying Algebraic Expressions 1 1 1 (1) Simplify the expression 2 + 1 . 3 3 4 2 y 3 )2 (x (2) Simplify the expression 3 2 2 . (y x ) 3 (3) Simplify (4x6 ) 2 . (4) If f (x) = x2 + 3x then simplify f (x + h) f (x)
School: UConn
Course: Calculus I
Worksheet 5: Applications of Derivatives Name: Section No: Derivatives and Graphs (1) For the following functions, use rst and second derivatives to determine (i) all points x where f (x) is a local maximum or minimum value, (ii) all open intervals where
School: UConn
Course: Calculus II
Math 1132 - Calculus 2 : Summary of convergence tests This is a guide for determining convergence or divergence of a series. You must be able to use these during exams. Series or Test Condition implying Convergence Form of the Series Condition implying Di
School: UConn
Course: Complex Function Theory I
Study guide for Ph.D. Examination in Complex Analysis (Math 5120) Holomorphic (analytic) functions: (1) (2) (3) (4) (5) Statement of the Jordan curve theorem and the notion of simple rectiable curves. The Riemann sphere. The Cauchy-Riemann equations. Powe
School: UConn
Study Guide for Risk Theory Prelim (MATH5637) 1. Modeling with random variables a. pf, pdf, cdf, ddf, hazard rate, moments (and related measures), quantiles b. generating functions and transforms: moment-, probability-, cumulant-; Fourier (characteristic)
School: UConn
Course: Calculus II
5/10/2015 Math1132Q,Spring2015 Math1132Q,Spring2015 Askingaquestionsometimesismoreimportantthanansweringaquestion.StayCurious! Instructor:TongZhu Email:tong.zhu(at)uconn.edu Office:113,UndergraduateBuilding Time:MON,WED10:00AM11:40AM OfficeHours:MON2:00PM
School: UConn
Course: Calculus I
5/14/2015 Math1131,CalculusI,Fall2013 Math1131Fall2013 CalculusI Section070 Links:SyllabusCommonCoursePageHuskyCTRecentAnnouncementsHandouts Instructor KeithConrad(Ifthisisnotyourinstructor,thisisnotapageforyoursectionofMath1131.) Email math1131courseatgm
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Spring 2015 TuTh 11:00AM - 12:15PM at MSB411 Math 3621 Actuarial Statistics Course Instructor Guojun Gan, PhD, ASA Oce: MSB 402 Email: Guojun.Gan@uconn.edu Oce Hours: TuTh 9
School: UConn
Course: Actuarial Mathematics I
Math 3630, Life Contingencies I, Fall 2014 Section 001, TTh 12:30-1:45 pm, MSB 411 Section 002, TTh 2:00-3:15 pm, MSB 411 Instructor Brian M. Hartman, PhD, ASA MSB 404 860.730.2700 brian.hartman@uconn.edu Office Hours: TTh 3:30-5:00 pm Grader Zhengpeng (Z
School: UConn
Course: CALCULUS II
CourseDescription 1132Q.CalculusII Fourcredits.Prerequisite:MATH1121,1126,1131,or1151,oradvancedplacementcredit forcalculus(ascoreof4or5ontheCalculusABexamorascoreof3orbetteronthe CalculusBCexam).Recommendedpreparation:AgradeofCorbetterinMATH1121 or1126or
School: UConn
Course: Actuarial Models
MATH 3634 - Actuarial Models Spring 2013 - Valdez Homework 1 Total marks: 100 due Friday, 22 February 2013, 6:00 PM Please write your name and student number at the spaces provided: Name: Student ID: Follow these instructions: There are ve (5) questions
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Final Report Actuarial Staffing Report Contents: Introduction.2 Salary. 2 Benefits.4 Exam Costs. 5 Exam Raises.7 Hiring/Replacing.9 Conclusion. 13 Mr. CFO, I have put together a well-developed and clearly articulated report on the companys lo
School: UConn
1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12), 1922, and 25. For brevity, the symbols R1, R2, stand for row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 2 x1 7 x2 = 5 1
School: UConn
Course: Elem Differential Equations
1. (10 points) Solve the initial Value problem %=yt+%, y(l)=3 iswt) 0') i g 5 41% ;S[cfw_+t)obt (2') KH!:?+aw|+a, gly 5=hf U) h:sef% i) (a) l D d 2. (15 points) Consider the differential equation dE; = where is given by the following graph (a) Sketch th
School: UConn
Course: Calculus II
5/10/2015 Math1132Q,Spring2015 Math1132Q,Spring2015 Askingaquestionsometimesismoreimportantthanansweringaquestion.StayCurious! Instructor:TongZhu Email:tong.zhu(at)uconn.edu Office:113,UndergraduateBuilding Time:MON,WED10:00AM11:40AM OfficeHours:MON2:00PM
School: UConn
Course: Calculus II
5/10/2015 Outline,Math1132Q,Spring2015 Outline,Math1132Q,Spring2015 Week Date 1 Jan21 2 Jan26,Jan28 3 4 5 6 7 8 9 10 Section 6.1 6.2,6.4 Feb2,Feb4 7.1,7.4 Feb9,Feb11 7.7,7.8 Feb16,Feb18 8.1,8.3 Feb23,Feb25 8.5,MidtermI 11.1,11.2, Mar2,Mar4 11.3 Mar9,Mar11
School: UConn
Course: Calculus I
MATH 1131 Calculus I No calculators. Show your work. Clearly mark each answer. 1. Find the equation of the tangent line at point (1, 1) for y 3 + x2 = 2. Solution: Assume that y is a function of x, i.e. y = y(x). Dierentiating both sides of the equation a
School: UConn
Course: Calculus I
MATH 1131 Calculus I No calculators. Show your work. Clearly mark each answer. 1. State the domain and the range of the function 1 x2 . Is this function one-to-one? Sketch the graph. Solution: Since the domain for x is x , the domain for 1 x2 is the set o
School: UConn
Course: Calculus I
5/14/2015 Math1131,CalculusI,Fall2013 Math1131Fall2013 CalculusI Section070 Links:SyllabusCommonCoursePageHuskyCTRecentAnnouncementsHandouts Instructor KeithConrad(Ifthisisnotyourinstructor,thisisnotapageforyoursectionofMath1131.) Email math1131courseatgm
School: UConn
Course: Calculus I
MATH 1131 Calculus I April 28, 2013 1. State the domain, range and possible symmetries of the following functions: (a) x2 + 1 Solution: Since x2 + 1 1, the domain is (, ), the range is [1, ). Since (x)2 + 1 the function is even. (b) x2 + 1 = x+1 Solution:
School: UConn
Course: Calculus I
MATH 1131 Calculus I 1. Find the linear approximation of 4 x at point a = 2 and using it estimate 4 16.04. Solution: The formula for the linear approximation is L(x) = f (16) + f (16)(x 16), 4 where f (x) = 4 x. Thus f (16) = 16 = 2 and f (16) = 1 163/4 =
School: UConn
Course: Calculus I
Worksheet 4: Derivatives Name: Section No: In the problems below, the parameters a, b, and c are constants. Use implicit dierentiation to dierentiate y with respect to x. (1) x2 y axy 2 = x + y (2) exy = x2 + y 2 (3) sin(x + y) = x + cos(3y) Use logarithm
School: UConn
Course: Calculus I
Worksheet on Limits Name: Discussion Section Number: 1. Tangent and velocity (2.1) The displacement (in meters) of an object moving in a straight line is given by 1 s = 1 + 2t + t2 , 4 where t is measured in seconds. (1) Find the average velocity over eac
School: UConn
Course: Calculus I
Worksheet 6: Integration Name: Section No: (1) Find the most general antiderivative of the function (use C as any constant). (a) f (x) = 1 3 2 4 3 + x x 2 4 5 t4 + 3 t (b) f (t) = t2 (c) g() = cos 5 sin (2) Find f (x) satisfying the given conditions. (a)
School: UConn
Course: Calculus I
Algebra Worksheet Name: Section No: 1. Simplifying Algebraic Expressions 1 1 1 (1) Simplify the expression 2 + 1 . 3 3 4 2 y 3 )2 (x (2) Simplify the expression 3 2 2 . (y x ) 3 (3) Simplify (4x6 ) 2 . (4) If f (x) = x2 + 3x then simplify f (x + h) f (x)
School: UConn
Course: Calculus I
Worksheet 5: Applications of Derivatives Name: Section No: Derivatives and Graphs (1) For the following functions, use rst and second derivatives to determine (i) all points x where f (x) is a local maximum or minimum value, (ii) all open intervals where
School: UConn
Course: Calculus I
Worksheet 3: Derivatives Name: Section No: Compute the derivatives of the following functions using the dierentiation rules up through section 3.4 (power rule, sum rule, product rule, quotient rule, chain rule). Parameters a, b, c, k, and n are constants.
School: UConn
Course: Calculus I
5/14/2015 TentativeOutlineforMath1131201314 TentativeOutlineforMath1131Fall2013 (Calculus,EarlyTranscendentals,byJamesStewart7thEdition) Week Date Section 1 2 3 Topic FourWaystoRepresentaFunction, andMathematicalModels NewFunctionsfromOldFunctions, 1.3,1.
School: UConn
Course: Fundamentals Of Algebra And Geometry
40 CHAPTER 1 Linear Equations in Linear Algebra Distribution of Output From: Purchased Chemicals Fuels .2 .3 .8 .1 .4 .4 Chemicals Fuels .5 output Machinery by: .1 .2 Machinery input b. Denote the total annual output (in dollars) of the sectors by pC, pF,
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.6 1.6 Solutions 39 SOLUTIONS 1. Fill in the exchange table one column at a time. The entries in a column describe where a sector's output goes. The decimal fractions in each column sum to 1. Distribution of Output From: Goods output Services input .7 .
School: UConn
Course: Fundamentals Of Algebra And Geometry
38 CHAPTER 1 Linear Equations in Linear Algebra 2 6 7 + x 21 and notice that the second column is 3 times the first. So suitable values for 33. Look at x1 2 3 9 3 x1 and x2 would be 3 and 1 respectively. (Another pair would be 6 and 2, etc.)
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.5 Solutions 35 2 The solution set is the line through 1 , parallel to the line that is the solution set of the homogeneous 0 system in Exercise 5. 16. Row reduce the augmented matrix for the system: 1 1 3 3 5 4 7 8 9 x1 + 4 x3 = 5 x2 3 x3 = 4
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.5 Solutions 37 c. True. If the zero vector is a solution, then b = Ax = A0 = 0. d. True. See the paragraph following Example 3. e. False. The statement is true only when the solution set of Ax = 0 is nonempty. Theorem 6 applies only to a consistent syst
School: UConn
Course: Fundamentals Of Algebra And Geometry
36 CHAPTER 1 Linear Equations in Linear Algebra The solution of x1 3x2 + 5x3 = 0 is x1 = 3x2 5x3, with x2 and x3 free. In vector form, x1 3 x2 5 x3 3x2 5 x3 3 5 x = x = x + 0 = x 1 + x 0 = x u + x v x = 2 2 3 2 2 3 2 x3 x3 0 x3 0 1 T
School: UConn
Course: Fundamentals Of Algebra And Geometry
34 CHAPTER 1 Linear Equations in Linear Algebra x1 5 x2 8 x4 x5 5 x2 8 x4 x5 8 1 5 x 0 x 0 0 1 x2 2 0 2 x 7 x4 4 x5 0 7 x4 4 x5 7 4 0 x = 3 = = + + = x2 + x4 + x5 x4 x4 1 0 0 x4 0 0 x5 0 1 0 0 x5 0 x5
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.5 Solutions 33 x1 3 x2 + 4 x4 3x2 0 4 x4 3 0 4 x x 0 0 1 0 x2 = 2 + + = x + x + x 0 x = 2 = 2 x3 0 x3 0 0 3 1 4 0 x3 x4 0 0 1 x4 0 0 x4 1 0 11. 0 0 4 2 0 3 5 0 0 1 0 0 0 0 1 1 4 0 0 0 0 0 x1 4 x2 x3 + 5 x6 = x
School: UConn
Course: Fundamentals Of Algebra And Geometry
32 CHAPTER 1 Linear Equations in Linear Algebra 3 5 4 7 1 6. 1 3 8 9 0 1 0 ~ 0 0 0 3 5 1 2 3 6 0 1 0 ~ 0 0 0 3 5 1 0 3 0 0 1 0 ~ 0 0 0 0 4 1 0 3 0 0 0 0 + 4 x3 = 0 x1 x2 3 x 3 = 0 . The variable x3 is free, x1 = 4x3, and x2 = 3x3. 0 = 0 x1
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.5 Solutions 31 For solving homogeneous systems, the text recommends working with the augmented matrix, although no calculations take place in the augmented column. See the Study Guide comments on Exercise 7 that illustrate two common student errors. All
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.4 Solutions 29 2 8 5 7 0 1.57 .429 3.29 , to three significant figures. The original matrix does not or, approximately 0 0 4.55 17.2 0 0 0 0 have a pivot in every row, so its columns do not span R4, by Theorem 4. 7 8 4 7 4 11 5 6 38. [M] 4 9 9
School: UConn
Course: Fundamentals Of Algebra And Geometry
30 CHAPTER 1 Linear Equations in Linear Algebra Note: Exercises 41 and 42 help to prepare for later work on the column space of a matrix. (See Section 2.9 or 4.6.) The Study Guide points out that these exercises depend on the following idea, not explicitl
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.4 Solutions 27 22. Row reduce the matrix [v1 v2 v3] to determine whether it has a pivot in each row. 0 4 2 8 5 0 0 3 1 ~ 0 3 1 2 8 5 0 0 4 The matrix [v1 v2 v3] has a pivot in each row, so the columns of the matrix span R4, by Theorem 4. That is,
School: UConn
Course: Fundamentals Of Algebra And Geometry
26 CHAPTER 1 1 ~ 0 0 3 7 0 Linear Equations in Linear Algebra 1 = 0 6 b2 + 3b1 0 b3 5b1 + 2(b2 + 3b1 ) 0 4 b1 3 7 0 6 b2 + 3b1 0 b1 + 2b2 + b3 4 b1 The equation Ax = b is consistent if and only if b1 + 2b2 + b3 = 0. The set of such b is a plane th
School: UConn
Course: Fundamentals Of Algebra And Geometry
28 CHAPTER 1 Linear Equations in Linear Algebra 29. Start with any 33 matrix B in echelon form that has three pivot positions. Perform a row operation (a row interchange or a row replacement) that creates a matrix A that is not in echelon form. Then A ha
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.4 x1 The solution is x2 x 3 Solutions 25 x1 0 = 3 . As a vector, the solution is x = x2 = 3 . x3 1 = 1 = 0 12. To solve Ax = b, row reduce the augmented matrix [a1 a2 a3 b] for the corresponding linear system: 1 3 0 1 ~ 0 0 2 1 1 5 2 3 2 0 5
School: UConn
Course: Fundamentals Of Algebra And Geometry
24 CHAPTER 1 Linear Equations in Linear Algebra For your information: The unique solution of this equation is (5, 7, 3). Finding the solution by hand would be time-consuming. Note: The skill of writing a vector equation as a matrix equation will be import
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.4 Solutions 23 2. The matrix-vector product Ax product is not defined because the number of columns (1) in the 31 2 5 matrix 6 does not match the number of entries (2) in the vector . 1 1 5 6 5 12 15 3 2 = 2 4 3 3 = 8 + 9 = 1 , and 3 3
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.3 Solutions 21 29. The total mass is 2 + 5 + 2 + 1 = 10. So v = (2v1 +5v2 + 2v3 + v4)/10. That is, 5 4 4 9 10 + 20 8 9 1.3 1 3 + 2 3 + 8 = 1 8 + 15 6 + 8 = .9 v= 2 4 + 5 10 10 3 2 1 6 6 10 2 + 6 0 30. Let m be the total mass o
School: UConn
Course: Fundamentals Of Algebra And Geometry
22 CHAPTER 1 Linear Equations in Linear Algebra The larger parallelogram shows that b is a linear combination of v1 and v3, that is, c4v1 + 0v2 + c3v3 = b So the equation x1v1 + x2v2 + x3v3 = b has at least two solutions, not just one solution. (In fact,
School: UConn
Course: Fundamentals Of Algebra And Geometry
20 CHAPTER 1 Linear Equations in Linear Algebra 25. a. There are only three vectors in the set cfw_a1, a2, a3, and b is not one of them. b. There are infinitely many vectors in W = Spancfw_a1, a2, a3. To determine if b is in W, use the method of Exercise
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.3 4 1 2 1 2 4 1 2 4 3 1 ~ 0 17. [a1 a2 b] = 5 15 ~ 0 1 2 7 h 0 3 h + 8 0 3 in Spancfw_a1, a2 when h + 17 is zero, that is, when h = 17. 4 1 3 ~ 0 h + 8 0 h 1 3 h 1 3 1 3 0 ~ 0 18. [v1 v2 y] = 5 ~ 0 1 5 1 1 2 8 3 0 2 3 + 2h 0 0
School: UConn
Course: Fundamentals Of Algebra And Geometry
18 CHAPTER 1 Linear Equations in Linear Algebra 1 0 2 5 M = 2 5 0 11 2 5 8 7 Row reduce M until the pivot positions are visible: 1 0 2 5 1 0 2 5 M ~ 0 5 4 1 ~ 0 5 4 1 0 5 4 3 0 0 0 2 The linear system corresponding to M has no solution, so the vec
School: UConn
Course: Calculus I
5/14/2015 TentativeOutlineforMath1131201314 TentativeOutlineforMath1131Fall2013 (Calculus,EarlyTranscendentals,byJamesStewart7thEdition) Week Date Section 1 2 3 Topic FourWaystoRepresentaFunction, andMathematicalModels NewFunctionsfromOldFunctions, 1.3,1.
School: UConn
Course: Financial Mathematics II
Math 3650 Chapter 24 Lecture notes Lets talk about bonds! Corporate Bonds are loans made by corporations to borrow money for investments and growth. Youve all had Math 2620 which teaches you how to price bonds (although Im going to complicate that as we g
School: UConn
Course: Actuarial Statistics
Math 3621 Project Details (similar to the model provided by Prof. Frees in his book and on his website) Overall Your report must be no more than 15 pages long (including all figures, tables, and appendices, 11 point font, spacing of at least 1.15, and 1 m
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 8: Autocorrelations and Autoregressive Models Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut March 31 & April 2, 2015 In this class, we will discuss the following topics Autocorrelations Aut
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 5: Variable Selection Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut Mar 3 and 5, 2015 In this chapter, we will discuss the following topics Automatic variable selection Residual analysis In
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 6: Interpreting Regression Results Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut Mar 10 and 12, 2015 In this class, we will discuss the following topic Interpretations of regression results
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 3: Multiple Linear Regression I Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut Feb 10 and 12, 2015 In this chapter, we will discuss the following topics The method of least squares Multiple
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 4: Multiple Linear Regression II Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut Feb 17 and 19, 2015 In this chapter, we will discuss the following topics Categorical variables Statistical in
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 1: Regression Analysis and Normal Distribution Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut Jan 20, 22, 27, 2015 In this chapter, we will cover the following topics An overview of regressi
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 2: Basic Linear Regression Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut Feb 3, 5, 2015 In this chapter, we will learn Correlations Least Squares Basic Linear Regression Models Variability
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 12: Count Dependent Variables Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut April 16 & 21, 2014 In this chapter, we will learn the following topics Poisson regression An application of Pois
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 11: Categorical Dependent Variables Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut April 14 & 16, 2014 In this chapter, we will learn the following topics Binary dependent variables Logistic
School: UConn
Course: Multivariable Calculus
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School: UConn
Course: Financial Mathematics Problems
Interest Functions v= 1 (1 + i ) d = 1 v = i= i = iv 1+ i d d = 1 d v i d = id = ln(1 + i ) Accumulation function: a (n) = (1 + i ) n = e n - for constant force of interest n (t ) dt a (n) = e 0 - for variable force of interest Definition of force of in
School: UConn
Course: Financial Mathematics Problems
TI Financial Calculator Functions TVM Workbook Underlying formula in familiar form: ( [ PV ] + m [ PMT ] anm ) + [ FV ] (1 + i ) n = 0 where: m = payments per year i = annual effective interest rate n = number of years of payments (= number of years betwe
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Fall 2013 11/14/13 Examples ACTEX Module 14 1 A farmer expects to grow and sell 100,000 bushels of wheat each year. In order to eliminate variability in the prices he will receive when se
School: UConn
Course: Financial Mathematics Problems
DERIVATIVES BACKGROUND INFORMATION Buying & Selling Stock Exchange stock stock pmt2 Broker pmt1 You (Buyer) stock pmt3 Broker stock pmt4 Seller pmt1 = ask price + broker commission pmt2 = ask price (price at which the market-maker is willing to sell the s
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Fall 2013 Examples Module 12 11/7/2013 1. Stock A is currently trading at 50. For each of the following situations, calculate the 1-year forward price and 1-year pre-paid forward price, g
School: UConn
Course: Programming For Actuaries
1) Some additional table basics Field Selection: Complex field types can be added in the "Design View" menu. In design view, type in a field name and select field type. In the properties window, specify the additional criteria for the added field. Standar
School: UConn
Course: Elem Differential Equations
February 18, 2013 Math 2410: Final Review Name: 1. Section 1.2: Use separation of variables to solve the following dierential equations. (a) dy dt =t3y (b) dy dt = (c) dy dt = (y 2 + 1)t , y(0) = 1 (d) dy dt = ty , y(0) = 3 t t2 y+y (e) A 5-gallon bucket
School: UConn
Course: Elem Differential Equations
I: I . - (glui'rws . WI we I F' "L" evml Salvhhm -JHR " 2 z - A- . m. "0%: N. b)? / XFUH) bh 2 3 0: ( Hf 94570 -=; (z-A)(eA)-("cfw_3(?)=O .) lZ'v-Z-A'LA +Az +gco 1H: sew; Cfiwgls a rm +2.0 -: H- 3 20) = 8': Jewgo -n= (-006) 2' /3 TLF'd-l-I : Xil, / cf
School: UConn
Course: Elem Differential Equations
HL WI 4 l 6 cfw_r-lit 50m) " -I-e 2 9 1" 4w - 2.6 )5? 3% I? _.- M 5H: 56 sf 5% [Twas fag A $16 +556 +378 f .2, 51+6S+57 :0 -.> CS+L)(5+4) = O _? : *2; "q -~ 46 "515 W 4, : me + K26 JPN Ho" MW") . 61:7 :H' 0% 319? fbg-cfw_ r8Y=a -s-E _3 -3-6 [71395-y:0cfw_
School: UConn
Course: Elem Differential Equations
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School: UConn
Course: Math For Business & Economics
Next week quiz: 6.1, 6.2, 6.3 (random variables, mean, variance) Lecture next week: compound interest and annuities- Chapter F Midterm 2 on Thursday April 17th, on: 4.6, 4.7, Chapter 5, Chapter 6, Chapter F- dont use the outline on the site Today: More no
School: UConn
Course: Math For Business & Economics
quiz on 2.2 and 1.3 2.3 inverse matrices If AB=BA=I then B= A^-1 Example: [3 1 5 2] has [2 -5 -1 3] as an inverse Multiply by each other and get [1 0 0 1] meaning yes it is an inverse because this is the identity
School: UConn
Course: Math For Business & Economics
No quiz this week Matrix quiz next week 2.2 Matrix Multiplication If R = [ r1, r2. rn] is a row matrix (1 X n) and C = [c1 is a colum matrix (n X 1) c2 cn] If the number of elements is the same then RC = [r1.rn] [c1 c2 cn] r1c1 +r2c2 + rncn Example: [5 2]
School: UConn
Course: Math For Business & Economics
Midterm 2 (info on site) No quiz this week Thursday night, same rooms as last time TLS Formulas from Chapter F F4: Amortization (Decreasing Annuity) Example: Find the monthly payment to pay off (amortize) a $100,000 loan over 40 years, at a rate of 8% (co
School: UConn
Course: Math For Business & Economics
Practice test posted on the site After class- download it tonight! 2 hour exam In lecture next week go over practice exam Mon/Wed Today F2 Compound Interest: Simple interest applies to principal F= P (1 +rt) = P+prt Compound interest applies to current
School: UConn
Course: Math For Business & Economics
Next Week: Quiz on 2.2 Matrix multiplication and 1.3 solving a system of equations 1.3 Gaussian Elimination: Recall a linear system of equations, like 1. x + 2y = 20 2. 2x + y =16 One method to solve for x and y is substitution Use equation 2 to solve for
School: UConn
Course: Math For Business & Economics
F3 Increasing Annuities (sinking funds) Increasing Annuity: Savings account with equal payments each period, subject to compound interest Given: Interest rate r, compounded m times a year, with equal payments PMT, after n periods the balance is future val
School: UConn
Course: Math For Business & Economics
Midterm Two: Next Thursday April 17th Practice exam posted this week 4.6, 4.7, Chapter 5, (5.3, 5.4) Chap 6- (6.4) Chap F- Finance Quiz this week on 6.1-6.3 on Random variables histograms F1 Simple Interest and Discounts: Principal: The initial amount of
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.4 Integration of Rational Functions by Partial Fractions In this section we will learn how to integrate rational functions by expressing them as a sum of simpler functions, called partial fractions, that we know how to in
School: UConn
Course: CALCULUS II
Chapter(11(Review(Notes( ( Chapter(11(is(on(Infinite(Sequences(and(Series.(We(begin(with(Sequences.( ( Sequences( Simply(put,(a(mathematical(sequence(is(a(set(of(numbersfor(example,(2,(4,(6,(8,(10( (designated(as(a(finite(sequence)(or(1,(,(,.(designated(a
School: UConn
Course: CALCULUS II
Chapter 10Parametric Equations and Polar Coordinates 10.4Areas and Lengths in Polar Coordinates In this section we will examine the area of a region whose boundary is given by a polar equation. For example, suppose we were interested in finding the area
School: UConn
Course: CALCULUS II
Chapter 10Parametric Equations and Polar Coordinates 10.1Curves Defined By Parametric Equations Suppose that !"#! are both given as functions of a third variable ! (called a parameter) by the equations ! = !(!) and ! = !(!) (called parametric equations).
School: UConn
Course: CALCULUS II
Ch. 11 Infinite Sequences and Series 11.2 Series % Suppose we are given some infinite sequence !"# $ #&' = "' , ") , "* , , "# , and were asked to add up its terms, that is, "' + ") , + + "# , This new expression, that is, "' + ") , + + "# , is called an
School: UConn
Course: CALCULUS II
Ch. 11 Infinite Sequences and Series 11.6 Absolute Convergence and the Ratio and Root Tests We begin this section by considering a series whose terms are the absolute values of the terms of the original series. Definition ! is called absolutely convergent
School: UConn
Course: CALCULUS II
Chapter 8Further Applications to Integration 8.3Applications to Physics and Engineering In this section we consider applications of the integral calculus to both physics and engineering. In particular, the applications to these areas will involve hydrost
School: UConn
Course: CALCULUS II
Ch. 11 Infinite Sequences and Series 11.1 Sequences A sequence can be thought of as a list of numbers written in a definite order. For example, 2, 4, 6, 8, 10. The sequence is said to be finite if there is a last number (e.g., in the example above) ! $ "
School: UConn
Course: CALCULUS II
Chapter 8Further Applications to Integration 8.5Probability As you know the probability that an event occurs is a number in the closed interval [0,1]that is, the probability that an event occurs can take on any number between 0 and 1 and including 0 or 1
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.8 Improper Integrals b In defining the definite integral f ( x)dx , the function f was assumed to be defined on a the closed interval [a, b]. We now extend the definition of the definite integral to consider an infinite
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.7 Approximate Integration b In evaluating a Definite Integral such as f ( x)dx , sometimes it is very difficult, or even a impossible, to find an antiderivative of f . As an example, it is impossible to evaluate the 1 2
School: UConn
Course: CALCULUS II
Chapter 6Applications of Integration 6.4Work Previously we learned that if ! ! represents the position of a particle at time ! then ! ! ! = !(!) that is, the first derivative of the position function represents the velocity of the particle at time ! and
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Initial Assessment Essay Risk is everywhere in the world today. With risk comes uncertainty. Not knowing what the future holds can be very daunting, especially in the business world. However, this is where actuaries excel. Actuaries are exper
School: UConn
Course: Actuarial Mathematics I
Math 3630 Life Contingencies I Chapter 6: Premiums Premiums Premiums are the amounts paid to the insurer in exchange for the benets provided to the insured. The premium may consist of one or more payments. In traditional life insurance contracts, the prem
School: UConn
Course: Actuarial Mathematics I
Math 3630 Life Contingencies I Chapter 4: Life insurance Review of (actuarial) interest theory notation We use i to denote an annual eective rate of interest. The one year present value (discount) factor is denoted by v = 1/(1 + i). i (m) is an annual nom
School: UConn
Course: Actuarial Mathematics I
Math 3630 Life Contingencies I Chapter 5: Life annuities Life annuities Here were going to consider the valuation of life annuities. A life annuity is regularly (e.g., continuously, annually, monthly, etc.) spaced series of payments, which are usually bas
School: UConn
Course: Actuarial Mathematics I
Chapter 1: Introduction Math 3630: Life Contingencies Brian M. Hartman, PhD ASA Overview Chapter 1 in the text gives a broad introduction to life insurance. Overview of the industry Definitions History Background Premium: Amount paid by the policy ho
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 7 Asset-Liability Management, Duration, and Immunization Duration (or Macaulay Duration) D or MacD The duration of a stream of payments is a weighted average of the number
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 6 - TERM STRUCTURE OF INTEREST RATES Spot Rate (sn) the level annual interest rate that applies to a currently-issued n-year zero-coupon bond Yield Curve spot rates for zer
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 5 - YIELD RATE OF AN INVESTMENT To find the internal rate of return (IRR) for a series of cash flows, solve the following equation for v: C0 + C1v + C 2 v 2 + Cn v n = 0 Th
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 4 - BONDS Definitions: F = face value or par value r = coupon rate (per coupon payment period) Fr = coupon amount n = number of coupon payment periods remaining until redem
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 3 - LOAN REPAYMENT Outstanding Loan Balance There are three methods for calculating the outstanding balance of a loan. The one to be used in a particular situation depends
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 2 - ANNUITIES a + a r + a r 2 + . + a r n 1 = a Finite Geometric series: a + a r + a r 2 + . = Infinite Geometric series: 1 rn r n 1 = a , where r 1 1 r r 1 a , where r <
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Summary Module 1 - INTEREST RATES a(t) is the accumulation function; it represents the accumulated value at time t of an investment of 1 unit that was made at time 0. A(t) is the amount f
School: UConn
Course: Programming For Actuaries
For your reference: Excel File Types Source Link Format Extension Description In other words Excel Workbook .xlsx Excel Workbook (code) .xlsm Excel Binary Workbook .xlsb Template .xltx Template (code) .xltm Excel 97- Excel 2003 Workbook .xls Excel 97- Exc
School: UConn
Course: Programming For Actuaries
1) Access Ribbon Review: Review the Access menu to show what options are available. (10 minutes) 2) Access - what is it for? Excel-based examples of where Access is a better fit. i) Access allows for linking of large tables that share some common fields.
School: UConn
Course: Programming For Actuaries
Sample Code for a Function Function ElfCount(lngHouses As Long, lngPresents As Long) 'This function, ElfCount, will give the number of 'elves required, given the number of houses and presents. Dim dblTemp As Double, dblTemp2 As Double dblTemp = lngHouses
School: UConn
Course: Programming For Actuaries
MATH 3550: PROGRAMMING FOR ACTUARIES Jim Head 08/27/2013 Course Set-up: This course is divided into 3 sections: Microsoft Excel / Spreadsheet Basics, Microsoft Access / Database Basics, Excel: Visual Basic for Applications/ Introduction to Programming
School: UConn
Course: Programming For Actuaries
Excel Menus: An Introduction MATH 3550 8/27/2013 The Button menu (2007), and File menu (2010): Left-click the button with MS Windows icon on the top left of your screen. This menu reveals workbook m enu item New, Open, Save, s: Print, Close also, at the
School: UConn
Course: Geometry
Chapter 3 Axioms for Plane Geometry 3.2 Distance and Ruler Postulate The next axiom addresses what is to be assumed regarding the undefined term, distance. Axiom 3.2.1 (The Ruler Postulate). For every
School: UConn
Course: Geometry
Chapter 3 Axioms for Plane Geometry 3.3 Plane Separation In this section we will examine how and line divides a plane into two half- planes, which will lead us to the definition of angle. We begin wit
School: UConn
Course: Geometry
Chapter 3 Axioms for Plane Geometry 3.7 The Parallel Postulates and Models The geometry that can be done using only the six postulates stated in this chapter is called neutral geometry. Absolute geomet
School: UConn
Course: Geometry
Chapter 3 Axioms for Plane Geometry 3.5 The Crossbar Theorem and the Linear Pair Theorem In this section we will state two fundamental theorems (without proof)the Crossbar Theorem and the Linear Pair Th
School: UConn
Course: Geometry
Chapter 2 Axiomatic Systems and Incidence Geometry 2.5 Theorems, Proof, and Logic At this point we examine the third part of an axiomatic systemthe theorems and proofs. It should be clear that a major
School: UConn
Course: Geometry
Chapter 3 Axioms for Plane Geometry 3.6 The Side-Angle-Side Postulate In this section we will examine the relationship between the length of segments and angle measure and the best way to do so is thr
School: UConn
Course: Geometry
Chapter 3 Axioms for Plane Geometry 3.4 Angle Measure and the Protractor Postulate In this section we discuss the last undefined termangle measure. Axiom 3.4.1 (The Protractor Postulate). For every
School: UConn
Course: Geometry
Chapter 2 Axiomatic Systems and Incidence Geometry 2.2 An Example: Incidence Geometry Next we give a more mathematical and rigorous example of what an axiomatic system is, the example of incidence geomet
School: UConn
Course: Geometry
Chapter 2 Axiomatic Systems and Incidence Geometry 2.3 The Parallel Postulates in Incidence Geometry The purpose of this section is to gain a better understanding of Euclids Fifth Postulate, referred to as
School: UConn
Course: Geometry
Chapter 1 Euclids Elements 1.0 Geometry Before Euclid The word Geometry comes from the Greek words geo which means earth and metron which means measurementthat is, the measurement of the earth. [It] is a
School: UConn
Course: Geometry
Chapter 3 Axioms for Plane Geometry Introduction In this chapter you will be introduced to six axioms, which will lay the foundation to all geometries studied throughout this course. Specifically, the geo
School: UConn
Course: Geometry
Chapter 2 Axiomatic Systems and Incidence Geometry 2.6 Some Theorems from Incidence Geometry We now have built up enough information to try and prove some theorems from incidence geometry. Since the theo
School: UConn
Course: Geometry
Chapter 2 Axiomatic Systems and Incidence Geometry 2.4 Axiomatic Systems and the Real World A nave view of geometry is that it is a branch of mathematics concerned with questions of shape, size, and t
School: UConn
Course: Geometry
Chapter 2 Axiomatic Systems and Incidence Geometry In this chapter we will examine the fundamental components of an axiomatic systemits parts and the relationship between its parts. We will explore an example o
School: UConn
Course: CALCULUS II
Math 1132 1. HW 5.5 / 6.2 Fall 12 4x3 dx 1 12x4 Solution: Let u = 1 12x4 . Then du = 48x3 dx and 2. du = 4x3 dx. So we have 12 1 4x3 du dx = 12 u 1 12x4 u 1 = +C 12 1/2 1 1 12x4 + C = 6 dx 9x + 1 Solution: Let u = 9x + 1. Then du = 9dx and dx 1 du = 9x +
School: UConn
Course: CALCULUS II
Math 1132 HW 6.3 Fall 12 1. Use the general slicing method to nd the volume of the solid with a base dened by the curve y = 12 sin x and the interval [0, ] on the x-axis. The cross-sections of this solid are squares perpendicular to the x-axis with bases
School: UConn
Course: CALCULUS II
Math 1132 HW 7.1 Fall 12 xe9x dx 1. Use integration by parts to evaulate Solution: Let u = x and dv = e9x dx. Then du = dx and v = 1/9e9x . By the integration by parts formula: udv = uv vdu gives xe9x dx = 1 9x 1 xe 9 9 e9x dx 1 9x 1 1 9x xe e +C 9 9 9
School: UConn
Course: CALCULUS II
Math 1132 HW 6.5 Fall 12 1. Find the arc length of the line y = 2x+4 on the interval [0, 3] using calculus Solution: Using the formula for the length of a curve on an interval: b L= 1 + f (x)dx a We get 3 1 + 22 dx L= 0 =3 5 2. Find the length of the curv
School: UConn
Course: CALCULUS II
Math 1132 HW 6.6 Fall 12 1. A 170 lb person compresses a bathroom scale 0.170 in. If the scale obeys Hookes law, how much work is done compressing the scale if a 100 lb person stands on it? Solution: First we need to solve for k: 170 = k(.17) gives k = 10
School: UConn
Course: CALCULUS II
Math 1132 HW 7.2 Fall 12 2 sin2 xdx 1. Solution : Use the half-angle formula: sin2 (x) = 1 (1 cos(2x) 2 So 2 sin2 xdx = (1 cos(2x)dx =x 2. 1 sin(2x) + C 2 cos3 (x)dx Solution : Split o a cos(x), giving cos3 (x) = cos(x) cos2 (x) Now use the trig identity
School: UConn
Course: CALCULUS II
Math 1132 HW 6.7 Fall 12 1. Dierentiate f (x) = ln(ln(4x) Solution: Use the chain rule: f (x) = 8 2. Evaluate 0 1 4 1 = ln 4x 4x x ln 4x 4x 1 dx x+1 Solution: Let u = x + 1. Then x = u 1 and du = dx. So we have 0 4x 1 dx = x+1 9 4(u 1) 1 du u 9 8 4u 5 du
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
09/10/2013' Intro to R Robert C. Zwick University of Connecticut Download R The software is freely available at:! http:/cran.r-project.org! Windows and Mac versions available Boot Up R version 3.0.1 (2013-05-16) - "Good Sport" Copyright (C) 2013 The R F
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 12 Count Dependent Variables Brian M. Hartman, PhD, ASA University of Connecticut 2 Poisson Distribution The Poisson distribution is used for counts and has probability mass function Pr = = , = 0,1,2, ! = ; = The Poisson distrib
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 11 Categorical Dependent Variables Brian M. Hartman, PhD, ASA University of Connecticut 2 Binary Dependent Variables We know how to handle categorical explanatory variables. What if you are interested in modeling a categorical respons
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 7 Modeling Trends Brian M. Hartman, PhD, ASA University of Connecticut 2 Definitions A process is a series of actions or operations that lead to a particular end. A stochastic process is a collection of random variables that quantify
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 1 Regression and the Normal Distribution Brian M. Hartman, PhD, ASA University of Connecticut 2 Galton (1885) Widely considered the birth of regression Galton looked at the heights of 928 adult children All female heights were multip
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 6 Interpreting Regression Results Brian M. Hartman, PhD, ASA University of Connecticut 2 Interpreting Individual Effects Substantive/Practical Significance Does a 1 unit change in x imply an economically meaningful change in y? Stati
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Final Report Actuarial Staffing Report Contents: Introduction.2 Salary. 2 Benefits.4 Exam Costs. 5 Exam Raises.7 Hiring/Replacing.9 Conclusion. 13 Mr. CFO, I have put together a well-developed and clearly articulated report on the companys lo
School: UConn
Course: Elem Differential Equations
1. (10 points) Solve the initial Value problem %=yt+%, y(l)=3 iswt) 0') i g 5 41% ;S[cfw_+t)obt (2') KH!:?+aw|+a, gly 5=hf U) h:sef% i) (a) l D d 2. (15 points) Consider the differential equation dE; = where is given by the following graph (a) Sketch th
School: UConn
Course: Calculus I
MATH 1131 Calculus I No calculators. Show your work. Clearly mark each answer. 1. Find the equation of the tangent line at point (1, 1) for y 3 + x2 = 2. Solution: Assume that y is a function of x, i.e. y = y(x). Dierentiating both sides of the equation a
School: UConn
Course: Calculus I
MATH 1131 Calculus I No calculators. Show your work. Clearly mark each answer. 1. State the domain and the range of the function 1 x2 . Is this function one-to-one? Sketch the graph. Solution: Since the domain for x is x , the domain for 1 x2 is the set o
School: UConn
Course: Calculus I
MATH 1131 Calculus I April 28, 2013 1. State the domain, range and possible symmetries of the following functions: (a) x2 + 1 Solution: Since x2 + 1 1, the domain is (, ), the range is [1, ). Since (x)2 + 1 the function is even. (b) x2 + 1 = x+1 Solution:
School: UConn
Course: Calculus I
MATH 1131 Calculus I 1. Find the linear approximation of 4 x at point a = 2 and using it estimate 4 16.04. Solution: The formula for the linear approximation is L(x) = f (16) + f (16)(x 16), 4 where f (x) = 4 x. Thus f (16) = 16 = 2 and f (16) = 1 163/4 =
School: UConn
Course: Fundamentals Of Algebra And Geometry
40 CHAPTER 1 Linear Equations in Linear Algebra Distribution of Output From: Purchased Chemicals Fuels .2 .3 .8 .1 .4 .4 Chemicals Fuels .5 output Machinery by: .1 .2 Machinery input b. Denote the total annual output (in dollars) of the sectors by pC, pF,
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.6 1.6 Solutions 39 SOLUTIONS 1. Fill in the exchange table one column at a time. The entries in a column describe where a sector's output goes. The decimal fractions in each column sum to 1. Distribution of Output From: Goods output Services input .7 .
School: UConn
Course: Fundamentals Of Algebra And Geometry
38 CHAPTER 1 Linear Equations in Linear Algebra 2 6 7 + x 21 and notice that the second column is 3 times the first. So suitable values for 33. Look at x1 2 3 9 3 x1 and x2 would be 3 and 1 respectively. (Another pair would be 6 and 2, etc.)
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.5 Solutions 35 2 The solution set is the line through 1 , parallel to the line that is the solution set of the homogeneous 0 system in Exercise 5. 16. Row reduce the augmented matrix for the system: 1 1 3 3 5 4 7 8 9 x1 + 4 x3 = 5 x2 3 x3 = 4
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.5 Solutions 37 c. True. If the zero vector is a solution, then b = Ax = A0 = 0. d. True. See the paragraph following Example 3. e. False. The statement is true only when the solution set of Ax = 0 is nonempty. Theorem 6 applies only to a consistent syst
School: UConn
Course: Fundamentals Of Algebra And Geometry
36 CHAPTER 1 Linear Equations in Linear Algebra The solution of x1 3x2 + 5x3 = 0 is x1 = 3x2 5x3, with x2 and x3 free. In vector form, x1 3 x2 5 x3 3x2 5 x3 3 5 x = x = x + 0 = x 1 + x 0 = x u + x v x = 2 2 3 2 2 3 2 x3 x3 0 x3 0 1 T
School: UConn
Course: Fundamentals Of Algebra And Geometry
34 CHAPTER 1 Linear Equations in Linear Algebra x1 5 x2 8 x4 x5 5 x2 8 x4 x5 8 1 5 x 0 x 0 0 1 x2 2 0 2 x 7 x4 4 x5 0 7 x4 4 x5 7 4 0 x = 3 = = + + = x2 + x4 + x5 x4 x4 1 0 0 x4 0 0 x5 0 1 0 0 x5 0 x5
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.5 Solutions 33 x1 3 x2 + 4 x4 3x2 0 4 x4 3 0 4 x x 0 0 1 0 x2 = 2 + + = x + x + x 0 x = 2 = 2 x3 0 x3 0 0 3 1 4 0 x3 x4 0 0 1 x4 0 0 x4 1 0 11. 0 0 4 2 0 3 5 0 0 1 0 0 0 0 1 1 4 0 0 0 0 0 x1 4 x2 x3 + 5 x6 = x
School: UConn
Course: Fundamentals Of Algebra And Geometry
32 CHAPTER 1 Linear Equations in Linear Algebra 3 5 4 7 1 6. 1 3 8 9 0 1 0 ~ 0 0 0 3 5 1 2 3 6 0 1 0 ~ 0 0 0 3 5 1 0 3 0 0 1 0 ~ 0 0 0 0 4 1 0 3 0 0 0 0 + 4 x3 = 0 x1 x2 3 x 3 = 0 . The variable x3 is free, x1 = 4x3, and x2 = 3x3. 0 = 0 x1
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.5 Solutions 31 For solving homogeneous systems, the text recommends working with the augmented matrix, although no calculations take place in the augmented column. See the Study Guide comments on Exercise 7 that illustrate two common student errors. All
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.4 Solutions 29 2 8 5 7 0 1.57 .429 3.29 , to three significant figures. The original matrix does not or, approximately 0 0 4.55 17.2 0 0 0 0 have a pivot in every row, so its columns do not span R4, by Theorem 4. 7 8 4 7 4 11 5 6 38. [M] 4 9 9
School: UConn
Course: Fundamentals Of Algebra And Geometry
30 CHAPTER 1 Linear Equations in Linear Algebra Note: Exercises 41 and 42 help to prepare for later work on the column space of a matrix. (See Section 2.9 or 4.6.) The Study Guide points out that these exercises depend on the following idea, not explicitl
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.4 Solutions 27 22. Row reduce the matrix [v1 v2 v3] to determine whether it has a pivot in each row. 0 4 2 8 5 0 0 3 1 ~ 0 3 1 2 8 5 0 0 4 The matrix [v1 v2 v3] has a pivot in each row, so the columns of the matrix span R4, by Theorem 4. That is,
School: UConn
Course: Fundamentals Of Algebra And Geometry
26 CHAPTER 1 1 ~ 0 0 3 7 0 Linear Equations in Linear Algebra 1 = 0 6 b2 + 3b1 0 b3 5b1 + 2(b2 + 3b1 ) 0 4 b1 3 7 0 6 b2 + 3b1 0 b1 + 2b2 + b3 4 b1 The equation Ax = b is consistent if and only if b1 + 2b2 + b3 = 0. The set of such b is a plane th
School: UConn
Course: Fundamentals Of Algebra And Geometry
28 CHAPTER 1 Linear Equations in Linear Algebra 29. Start with any 33 matrix B in echelon form that has three pivot positions. Perform a row operation (a row interchange or a row replacement) that creates a matrix A that is not in echelon form. Then A ha
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.4 x1 The solution is x2 x 3 Solutions 25 x1 0 = 3 . As a vector, the solution is x = x2 = 3 . x3 1 = 1 = 0 12. To solve Ax = b, row reduce the augmented matrix [a1 a2 a3 b] for the corresponding linear system: 1 3 0 1 ~ 0 0 2 1 1 5 2 3 2 0 5
School: UConn
Course: Fundamentals Of Algebra And Geometry
24 CHAPTER 1 Linear Equations in Linear Algebra For your information: The unique solution of this equation is (5, 7, 3). Finding the solution by hand would be time-consuming. Note: The skill of writing a vector equation as a matrix equation will be import
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.4 Solutions 23 2. The matrix-vector product Ax product is not defined because the number of columns (1) in the 31 2 5 matrix 6 does not match the number of entries (2) in the vector . 1 1 5 6 5 12 15 3 2 = 2 4 3 3 = 8 + 9 = 1 , and 3 3
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.3 Solutions 21 29. The total mass is 2 + 5 + 2 + 1 = 10. So v = (2v1 +5v2 + 2v3 + v4)/10. That is, 5 4 4 9 10 + 20 8 9 1.3 1 3 + 2 3 + 8 = 1 8 + 15 6 + 8 = .9 v= 2 4 + 5 10 10 3 2 1 6 6 10 2 + 6 0 30. Let m be the total mass o
School: UConn
Course: Fundamentals Of Algebra And Geometry
22 CHAPTER 1 Linear Equations in Linear Algebra The larger parallelogram shows that b is a linear combination of v1 and v3, that is, c4v1 + 0v2 + c3v3 = b So the equation x1v1 + x2v2 + x3v3 = b has at least two solutions, not just one solution. (In fact,
School: UConn
Course: Fundamentals Of Algebra And Geometry
20 CHAPTER 1 Linear Equations in Linear Algebra 25. a. There are only three vectors in the set cfw_a1, a2, a3, and b is not one of them. b. There are infinitely many vectors in W = Spancfw_a1, a2, a3. To determine if b is in W, use the method of Exercise
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.3 4 1 2 1 2 4 1 2 4 3 1 ~ 0 17. [a1 a2 b] = 5 15 ~ 0 1 2 7 h 0 3 h + 8 0 3 in Spancfw_a1, a2 when h + 17 is zero, that is, when h = 17. 4 1 3 ~ 0 h + 8 0 h 1 3 h 1 3 1 3 0 ~ 0 18. [v1 v2 y] = 5 ~ 0 1 5 1 1 2 8 3 0 2 3 + 2h 0 0
School: UConn
Course: Fundamentals Of Algebra And Geometry
18 CHAPTER 1 Linear Equations in Linear Algebra 1 0 2 5 M = 2 5 0 11 2 5 8 7 Row reduce M until the pivot positions are visible: 1 0 2 5 1 0 2 5 M ~ 0 5 4 1 ~ 0 5 4 1 0 5 4 3 0 0 0 2 The linear system corresponding to M has no solution, so the vec
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.3 Solutions 3 2 3 (2)(2) 3 + (4) 1 u 2 v = + (2) = + = = , or, more quickly, 2 1 2 (2)(1) 2 + 2 4 3 2 3 4 1 u 2v = 2 = = . The intermediate step is often not written. 2 1 2 + 2 4 3. x2 u 2v uv u 2v u+v v x1 v 4. u 2v x2 uv u 2v u+v v x1 v
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.3 Solutions 17 Note: The Study Guide says, Check with your instructor whether you need to show work on a problem such as Exercise 9. = 9 = 2 , = 15 4 x1 + x2 + 3 x3 9 x 7x 2x = 2 2 3 1 8 x1 + 6 x2 5 x3 15 4 x1 x2 3x3 9 x1 + 7 x2 + 2 x
School: UConn
Course: Fundamentals Of Algebra And Geometry
16 CHAPTER 1 Linear Equations in Linear Algebra b. To reach b from the origin, travel 2 units in the u-direction and 2 units in the v-direction. So b = 2u 2v. Or, use the fact that b is 1 unit in the u-direction from a, so that b = a + u = (u 2v) + u = 2u
School: UConn
Course: Fundamentals Of Algebra And Geometry
10 CHAPTER 1 Linear Equations in Linear Algebra 4 2 x1 = 3 x2 3 x3 Basic variable: x1; free variables x2, x3. General solution: x2 is free x is free 3 1 12. 0 1 7 0 6 0 7 1 4 2 2 5 1 3 ~ 0 7 0 x1 7 0 6 0 0 1 4 2 8 7 x2 x3 Corresponding system: 5
School: UConn
Course: Fundamentals Of Algebra And Geometry
14 CHAPTER 1 Linear Equations in Linear Algebra 1 0 0 ~ 0 0 0 0 2 0 0 0 0 0 4 8 0 0 0 0 8 48 48 0 0 0 16 224 576 384 0 0 32 960 4800 7680 3840 1 0 0 ~ 0 0 0 0 2 0 0 0 0 0 4 8 0 0 0 0 8 48 48 0 0 0 16 224 576 384 0 0 0 0 0 0 1 0 1 2.9 0 9 0 ~ 3.9 0 6.9 0
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.2 Solutions 13 32. According to the numerical note in Section 1.2, when n = 30 the reduction to echelon form takes about 2(30)3/3 = 18,000 flops, while further reduction to reduced echelon form needs at most (30)2 = 900 flops. Of the total flops, the ba
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.2 + 7 x3 x1 x2 6 x3 Solutions = 9 = = 2 0 0 = Corresponding system: 3 x4 0 x5 x1 = 9 7 x3 x = 2 + 6 x + 3x 3 4 2 Basic variables: x1, x2, x5; free variables: x3, x4. General solution: x3 is free x is free 4 x5 = 0 15. a. The system is consistent
School: UConn
Course: Fundamentals Of Algebra And Geometry
12 CHAPTER 1 Linear Equations in Linear Algebra 22. a. False. See the statement preceding Theorem 1. Only the reduced echelon form is unique. b. False. See the beginning of the subsection Pivot Positions. The pivot positions in a matrix are determined com
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.2 1 8. 2 4 7 7 1 ~ 10 0 0 0 4 1 7 1 ~ 4 0 0 0 Corresponding system of equations: 4 1 7 1 ~ 4 0 0 0 0 1 0 0 Solutions 9 9 4 = 9 = 4 x1 x2 The basic variables (corresponding to the pivot positions) are x1 and x2. The remaining variable x3 is free.
School: UConn
Course: Fundamentals Of Algebra And Geometry
8 CHAPTER 1 1.2 Linear Equations in Linear Algebra SOLUTIONS Notes: The key exercises are 120 and 2328. (Students should work at least four or five from Exercises 714, in preparation for Section 1.5.) 1. Reduced echelon form: a and b. Echelon form: d. Not
School: UConn
Course: Fundamentals Of Algebra And Geometry
6 CHAPTER 1 Linear Equations in Linear Algebra 7 g 1 4 7 g 1 4 7 g 1 4 0 ~ 0 ~ 0 25. 3 5 h 3 5 h 3 5 h 2 5 9 k 0 3 5 k + 2 g 0 0 0 k + 2 g + h Let b denote the number k + 2g + h. Then the third equation represented by the augmented matrix above
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.1 Solutions 7 Rearranging, 4T1 T1 + T2 4T2 T2 T3 + 4T3 T3 T1 T4 T4 + 4T4 = = = = 30 60 70 40 34. Begin by interchanging R1 and R4, then create zeros in the first column: 4 1 0 1 1 4 1 0 1 0 1 4 0 1 4 1 30 1 60 1 ~ 70 0 40 4 1 1 4 0 0 4 1 1 4 0
School: UConn
Course: Fundamentals Of Algebra And Geometry
4 CHAPTER 1 1 13. 2 0 1 ~ 0 0 1 14. 1 0 1 ~ 0 0 Linear Equations in Linear Algebra 0 3 2 1 9 5 8 1 7 ~ 0 2 0 0 3 1 0 5 1 3 0 1 1 5 1 3 0 1 0 1 1 8 1 2 ~ 0 1 0 5 1 2 ~ 0 0 0 5 1 0 ~ 0 1 0 0 3 2 1 15 5 0 0 1 0 0 1 3 0 2 1 5 1 3 0 1 0 0 1 0
School: UConn
Course: Fundamentals Of Algebra And Geometry
1.1 Solutions 5 17. Row reduce the augmented matrix corresponding to the given system of three equations: 1 1 4 1 1 4 1 1 4 2 1 3 ~ 0 ~ 0 7 5 7 5 1 3 4 0 7 5 0 0 0 The system is consistent, and using the argument from Example 2, there is only o
School: UConn
Course: Actuarial Models
MATH 3634 - Actuarial Models Spring 2013 - Valdez Homework 1 Total marks: 100 due Friday, 22 February 2013, 6:00 PM Please write your name and student number at the spaces provided: Name: Student ID: Follow these instructions: There are ve (5) questions
School: UConn
Course: Calculus I
Worksheet 4: Derivatives Name: Section No: In the problems below, the parameters a, b, and c are constants. Use implicit dierentiation to dierentiate y with respect to x. (1) x2 y axy 2 = x + y (2) exy = x2 + y 2 (3) sin(x + y) = x + cos(3y) Use logarithm
School: UConn
Course: Calculus I
Worksheet on Limits Name: Discussion Section Number: 1. Tangent and velocity (2.1) The displacement (in meters) of an object moving in a straight line is given by 1 s = 1 + 2t + t2 , 4 where t is measured in seconds. (1) Find the average velocity over eac
School: UConn
Course: Calculus I
Worksheet 6: Integration Name: Section No: (1) Find the most general antiderivative of the function (use C as any constant). (a) f (x) = 1 3 2 4 3 + x x 2 4 5 t4 + 3 t (b) f (t) = t2 (c) g() = cos 5 sin (2) Find f (x) satisfying the given conditions. (a)
School: UConn
Course: Calculus I
Algebra Worksheet Name: Section No: 1. Simplifying Algebraic Expressions 1 1 1 (1) Simplify the expression 2 + 1 . 3 3 4 2 y 3 )2 (x (2) Simplify the expression 3 2 2 . (y x ) 3 (3) Simplify (4x6 ) 2 . (4) If f (x) = x2 + 3x then simplify f (x + h) f (x)
School: UConn
Course: Calculus I
Worksheet 5: Applications of Derivatives Name: Section No: Derivatives and Graphs (1) For the following functions, use rst and second derivatives to determine (i) all points x where f (x) is a local maximum or minimum value, (ii) all open intervals where
School: UConn
Course: Calculus I
Worksheet 3: Derivatives Name: Section No: Compute the derivatives of the following functions using the dierentiation rules up through section 3.4 (power rule, sum rule, product rule, quotient rule, chain rule). Parameters a, b, c, k, and n are constants.
School: UConn
Course: Financial Mathematics II
Math 3650 Chapter 24 Problems and Solutions 1. What is an indenture? 2. What is an original issue discount bond (OID)? 3. What are two types of unsecured corporate debt? What does this mean? 4. What are mortgage bonds? 5. What are asset-backed bonds? 6. W
School: UConn
Course: Financial Mathematics II
Math 3650 Fall 2014 Homework for Chapter 10 1. A common measure of the risk of a security is its volatility. Other measures of risk used in special situations (possibly insurance!) are semi-variance, and expected tail loss. Briefly define these 3 risk mea
School: UConn
Course: Financial Mathematics II
Math 3650 Practice Problems - Chapters 4,7, 8 and term project 1. Define Internal Rate of Return (IRR). Define the Opportunity Cost of Capital. If the IRR equals the opportunity cost of capital, what is the Net Present Value of the project calculated usin
School: UConn
Course: Financial Mathematics II
Chapter 9 Review Questions Math 3650 1. What is a firms Equity Cost of Capital? 2. Describe the Dividend Discount Model for valuing a firms stock price? What key conclusion does this lead to concerning investment decisions for a firm? 3. What is the Total
School: UConn
Course: Financial Mathematics II
Chapter 5 Review Questions Math 3650 1. Some examples of interest rate risk that insurance companies face are: Prepayment risk Market Risk Disintermediation Risk 2. List 5 factors that influence interest rates. 3. Briefly define the following key short te
School: UConn
Course: Financial Mathematics II
Math3650PracticeProblemsChapter3 1. How should the costs and benefits of a project be compared? In particular, what decision rule should financial managers use to compare costs and benefits? 2. If you could finance a project at the risk free rate, how wou
School: UConn
Course: Financial Mathematics II
Homework problems Chapter 6 and Duration 1. Current spot rates for US Treasuries are given below. Calculate the yield to maturity for a $1000 5 year US Treasury note paying 7% annual coupons. The redemption value and par value both equal $1000. Term Spot
School: UConn
Course: Financial Mathematics II
Math 3650 Practice Problems Chapter 2 1 The 10-Q and 10-K financial reports are produced under what accounting standards? 2 What are the 3 main statements in the 10-Q and 10-K? Briefly describe them. 3 How is Stockholders Equity (also known as Book Value
School: UConn
Course: Financial Mathematics II
Math 3650 Practice Problems - Chapters 1 1.As measured by the total number of firms, what is the most common type of business structure in the U.S.? 2.Most large businesses are organized under what type of business structure? 3.What are the advantages and
School: UConn
Course: Actuarial Mathematics II
SSSM-Calculator A 0.0002200 B 2.70E-06 cc 1.1240000 Notes: v d i(m) d(m) d select factor Interest Rate i Payment Frequency m 0.9 5.000% 12 1. All functions on annuity and insurance worksheets use this interest rate. 2. Interest rates and payment frequency
School: UConn
Course: Actuarial Mathematics II
SUSM-Calculator A 0.0001000 B 3.00E-04 cc 1.0750000 Notes: v d i(m) d(m) d Interest Rate i Payment Frequency m 5.000% 12 1. All functions on annuity and insurance worksheets use this interest rate. 2. Interest rates and payment frequency are displayed on
School: UConn
Course: Actuarial Mathematics II
h 0.08333333 12*t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 8
School: UConn
Course: Actuarial Mathematics I
SSSM-Calculator A 0.0002200 B 2.70E-06 cc 1.1240000 Notes: v d i(m) d(m) d select factor Interest Rate i Payment Frequency m 0.9 5.000% 12 1. All functions on annuity and insurance worksheets use this interest rate. 2. Interest rates and payment frequency
School: UConn
Course: Actuarial Mathematics I
SSSM-Calculator A 0.0002200 B 2.70E-06 cc 1.1240000 Notes: v d i(m) d(m) d select factor Interest Rate i Payment Frequency m 0.9 5.000% 12 1. All functions on annuity and insurance worksheets use this interest rate. 2. Interest rates and payment frequency
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2014 Homework Assignment 7 Due Date: Thursday, May 1, 2014 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. For Part II, you should use
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Fall 2014 MWF 10:10 11:00 at LH107 Homework 8 Exercise 1. Do Exercise 8.1 of the textbook. (10 points) Solution 1. (a). r1 = 0.2686 (b). r2 = 0.0821 (The answer in the textb
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Fall 2014 Homework 5 Exercise 1. Do Exercise 5.1 of the textbook. (10 points for each part. 30 points in total.) Solution 1. (a). Let 1 x1 1 x2 X = . . . . . . . 1 xn By d
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Fall 2014 Homework 4 Exercise 1. Do Exercise 4.1 of the textbook. (10 points for each part, 50 points in total) Solution 1. (a). R2 = SSR = 1 SST SSE . SSE+SSR (b). In this
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Fall 2014 MWF 10:10 11:00 at ITE125 Homework 3 Exercise 1. Do Exercise 3.2 in the textbook. (5 points for each part a,b,c,d. Total 20 points.) Solution 1. (a). se(b3 ) = s 4
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Fall 2014 MWF 10:10 11:00 at LH107 Homework 2 Exercise 1. Do Exercise 2.7 in the textbook. Solution 1. (a). (5 points) We can write SS(b ) as 1 n n SS(b ) 1 = (b )2 1 x2 i 2
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Fall 2014 Homework 6 Exercise 1. Do Exercise 6.1 of the textbook. (10 points for each part or subpart. 100 points in total.) Solution 1. See p538 of the textbook. Exercise 2
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Fall 2014 MWF 10:10 11:00 at LH107 Homework 7 Exercise 1. Do Exercise 7.1 of the textbook. (10 points for each part. 20 points in total) Solution 1. See p539 of the textbook
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Fall 2014 MWF 10:10 11:00 at LH107 Homework 1 Exercise 1. Let R = (, ) and let f : R [0, ) be dened as 1 2 1 f (x) = e 2 x . 2 (a). Show that f (x) is a probability density
School: UConn
Course: Actuarial Statistics
Solutions to Homework Problems of Math 3621 Actuarial Statistics Guojun Gan April 16, 2015 The R code used to solve the homework problems can be found at the end of this document. 1 1.1 Homework 1 Exercise 1.3 The histogram of the amount PAID is shown in
School: UConn
Course: Actuarial Statistics
Math 3621 Final Project Grade Sheet Group: Score _ _ _ Possible Presentation Own Presentation Attendance at classmates presentations Overall Presentation 10 5 15 Paper Grammar/Spelling/General Flow 10 Abstract/Executive Summary 5 Introduction 5 Data Chara
School: UConn
Course: Actuarial Statistics
Math 3621 Actuarial Statistics Chapter 7: Modeling Trends Guojun Gan, PhD, ASA Department of Mathematics University of Connecticut March 24 & 25, 2015 In this class, we will discuss the following topics Time series Modeling trends Random walk models Infer
School: UConn
Course: Actuarial Statistics
Homework Math3621 Actuarial Statistics Spring 2015 TuTh 11:00AM - 12:15PM at MSB411 Homework 1 Chapter 1: Exercises 1.3, 1.4. Chapter 2: Exercises 2.10, 2.20. Due: Feb 10, 5pm Homework 2 Chapter 3: Exercises 3.2, 3.5. Chapter 4: Exercises 4.1, 4.2. Due: F
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2014 Homework Assignment 6 Due Date: Thursday December 4, 2:00 pm Part I 1. You are using the Equivalence Principle to price a $100, 000 20 year term policy issued to (50). You are given the following: A50:20 = 0.4 v = 0.95 20 p50 = 0.9 (a)
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2014 Solutions to Homework Assignment 1 Due: September 16th at 2:00 pm 1. Jimmy recently purchased a house for he and his family to live in with a $300,000 30-year mortgage. He is worried that should he die before the mortgage is paid, his
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2014 Homework Assignment 6 Due Date: Tuesday, April 8, 2014 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. For Part II, you should us
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2014 Homework Assignment 5 Due Date: Tuesday, March 25, 2014 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. Your answers should consi
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2015 Homework Assignment 6 Due Date: Tuesday, April 14, 2015 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. For Part II, you should u
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2015 Homework Assignment 7 Due Date: Tuesday, April 28, 2015 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. For Part II, you should u
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2015 Homework Assignment 5 Due Date: Tuesday, March 31, 2015 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. Your answers should consi
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2014 Homework Assignment 4 Due Date: Tuesday, March 11, 2014 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. For Part II, you should u
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2015 Homework Assignment 4 Due Date: Tuesday, March 24, 2015 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. For Part II, you should u
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2014 Homework Assignment 2 Due Date: Tuesday, February 18, 2014 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. For Part II, you shoul
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2015 Homework Assignment 3 Due Date: Tuesday, March 3, 2015 General Notes: Please hand in your homework in class on the due date. In order to get full credit, you must show ALL work. For Part II, you should use a spreadsheet. Email the
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2015 Homework Assignment 2 Due Date: Tuesday, February 17, 2015 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. For Part II, you shoul
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2014 Homework Assignment 3 Due Date: Friday, February 28, 2014 at noon (moved one day because of 3621 exam) General Notes: Please hand in your homework either in class before the due date or to my oce (404 MSB) by noon on the due date. I
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2014 Homework Assignment 1 Due Date: Tuesday, February 4, 2014 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. Your answers should con
School: UConn
Course: Actuarial Mathematics II
Math 3631 Spring 2015 Homework Assignment 1 Due Date: Tuesday, February 3, 2015 General Notes: Please hand in your homework on paper, at the beginning of class on the due date. In order to get full credit, you must show ALL work. Your answers should con
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Fall 2013 Name Homework Assignment 8 due Tuesday 11/19/13 1. A stock is currently trading at 105. The continuously compounded risk-free interest rate is 0.06. For each of the following si
School: UConn
Course: Financial Mathematics Problems
University of Connecticut Math 3615: Financial Mathematics Problems Fall 2013 Name Homework Assignment 6 due Tuesday 10/24/13 1. Stock A, a non-dividend-paying stock, traded at the following prices per share at each of the indicated times: Time (in years)
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 2 1. Exercise 3.2.1 If and m are two lines, the number of points in m is either 0, 1, or . Proof: Let and m be two lines. Either these lines are parallel or they are not. If m, then and m have 0 intersection po
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 1 SOLUTIONS 1. Exercise 2.4.1 Solution: This is not a model for incidence geometry since it does not satisfy Axiom 3. There is no set of three beer mugs (points) that do not all lie on the same table (line). Th
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 11 MATH 3160 - Probability - Fall 2014 Assignment 11 (Due Wednesday, December 3, at the beginning of class) NO LATE SUBMISSION. Your graded assignments will be returned in class on Friday, December 5. Relevant
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 10 MATH 3160 - Probability - Fall 2014 Assignment 10 (Due Wednesday, November 19, at the beginning of class) Relevant sections: Ross, 7.27.5. Please show all work. Justify your numerical answer with brief expl
School: UConn
Course: Calculus II
Math 1132 - Calculus 2 : Summary of convergence tests This is a guide for determining convergence or divergence of a series. You must be able to use these during exams. Series or Test Condition implying Convergence Form of the Series Condition implying Di
School: UConn
Course: Complex Function Theory I
Study guide for Ph.D. Examination in Complex Analysis (Math 5120) Holomorphic (analytic) functions: (1) (2) (3) (4) (5) Statement of the Jordan curve theorem and the notion of simple rectiable curves. The Riemann sphere. The Cauchy-Riemann equations. Powe
School: UConn
Study Guide for Risk Theory Prelim (MATH5637) 1. Modeling with random variables a. pf, pdf, cdf, ddf, hazard rate, moments (and related measures), quantiles b. generating functions and transforms: moment-, probability-, cumulant-; Fourier (characteristic)
School: UConn
Course: Calculus II
5/10/2015 Math1132Q,Spring2015 Math1132Q,Spring2015 Askingaquestionsometimesismoreimportantthanansweringaquestion.StayCurious! Instructor:TongZhu Email:tong.zhu(at)uconn.edu Office:113,UndergraduateBuilding Time:MON,WED10:00AM11:40AM OfficeHours:MON2:00PM
School: UConn
Course: Calculus I
5/14/2015 Math1131,CalculusI,Fall2013 Math1131Fall2013 CalculusI Section070 Links:SyllabusCommonCoursePageHuskyCTRecentAnnouncementsHandouts Instructor KeithConrad(Ifthisisnotyourinstructor,thisisnotapageforyoursectionofMath1131.) Email math1131courseatgm
School: UConn
Course: Actuarial Statistics
Department of Mathematics University of Connecticut Math3621 Actuarial Statistics Spring 2015 TuTh 11:00AM - 12:15PM at MSB411 Math 3621 Actuarial Statistics Course Instructor Guojun Gan, PhD, ASA Oce: MSB 402 Email: Guojun.Gan@uconn.edu Oce Hours: TuTh 9
School: UConn
Course: Actuarial Mathematics I
Math 3630, Life Contingencies I, Fall 2014 Section 001, TTh 12:30-1:45 pm, MSB 411 Section 002, TTh 2:00-3:15 pm, MSB 411 Instructor Brian M. Hartman, PhD, ASA MSB 404 860.730.2700 brian.hartman@uconn.edu Office Hours: TTh 3:30-5:00 pm Grader Zhengpeng (Z
School: UConn
Course: CALCULUS II
CourseDescription 1132Q.CalculusII Fourcredits.Prerequisite:MATH1121,1126,1131,or1151,oradvancedplacementcredit forcalculus(ascoreof4or5ontheCalculusABexamorascoreof3orbetteronthe CalculusBCexam).Recommendedpreparation:AgradeofCorbetterinMATH1121 or1126or
School: UConn
Course: CALCULUS II
CourseDescription 1132Q.CalculusII Four credits.Prerequisite:MATH 1121,1126,1131,or 1151,or advancedplacementcreditfor calculus(a scoreof 4 or 5 on the CalculusAB examor a scoreof 3 or betteron theCalculusBC exam). Recommendedpreparation:A gradeof C- or b
School: UConn
Course: Problem Solving
Math 1020Q Group Projects (Great American Road Trip) Collectively as a class, we will plan a 10-week driving trip around the continental United States, also known as the Great American Road Trip. Each group will have one of the regions on the back and the
School: UConn
Course: Problem Solving
PROBLEM SOLVING MATH 1020Q Section 003 SYLLABUS Meeting Times: MWF, 2:00pm 2:50pm in MSB219 Textbook: PProblem SSSolving, 2nd Edition, by DeFranco and Vinsonhaler Ben Brewer, MSB201 Email: benjamin.a.brewer
School: UConn
Course: Problem Solving
PROBLEM SOLVING MATH 1020Q Section 002 SYLLABUS Meeting Times: MWF, 10:00am 10:50am in MSB303 Textbook: PProblem SSSolving, 2nd Edition, by DeFranco and Vinsonhaler Ben Brewer, MSB201 Email: benjamin.a.brew
School: UConn
Course: Financial Mathematics I
University of Connecticut Financial Mathematics I - Math 2620/5620 Syllabus - Fall 2011 (revised 9/12/2011) Welcome to Financial Math! This is an important foundation course in actuarial science and finance, with two principal goals for students: The firs
School: UConn
Spring 2009 Math 2110Q, Section 02 Class meets MWF 11:00 am -12:15 pm in MSB 307. Text: J. Stewart, Multivariable Calculus: Early Transcendentals, 6th edition. Instructor: Wally Madych, MSB 308 O. Hours: MWF 10-11 am, 1-2 pm, and by arrangement. Cont
School: UConn
University of Connecticut Advanced Financial Mathematics Math 5660(324) Spring 2009 Classes: MWF: 1:00 1:50 MSB415 Instructor: James G. Bridgeman, FSA MSB408 Office Hours: M 11:00 12:00 860-486-8382 W 5:00 6:00 bridgeman@math.uconn.edu Th/F 10:00