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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: Geometry
MATH 2360Q UNIVERSITY OF CONNECTICUT SPRING 2014 MIDTERM EXAM 1 Name: This exam consists of two parts. The rst part is an in class portion and consists of 5 questions and you will have the duration of the class period to complete it. The second part is a
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: 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: 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: 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: 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: Geometry
MATH 2360Q UNIVERSITY OF CONNECTICUT SPRING 2014 MIDTERM EXAM 1 Name: This exam consists of two parts. The rst part is an in class portion and consists of 5 questions and you will have the duration of the class period to complete it. The second part is a
School: UConn
Course: Probability
MATH 3160 - Fall 2013 Practice Midterm Exam 1 Solutions MATH 3160 - Probability - Fall 2013 Practice Midterm Exam 1 Solutions 1. For each of the following statements, determine whether it is true (T) or false (F): (a) There are 180 dierent arrangements of
School: UConn
Course: Probability
MATH 3160 - Fall 2013 Practice Midterm Exam 1 MATH 3160 - Probability - Fall 2013 Practice Midterm Exam 1 Instructions: Each of the n problems below is worth the same. You MUST answer the T/F questions in Problem 1. For this problem, only the nal answer
School: UConn
Course: Probability
NAME: Spring 2014 18.440 Final Exam: 100 points Carefully and clearly show your work on each problem (without writing anything that is technically not true) and put a box around each of your nal computations. 1. (10 points) Let X be a uniformly distribute
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: 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: 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: 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: Geometry
MATH 2360Q UNIVERSITY OF CONNECTICUT SPRING 2014 MIDTERM EXAM 1 Name: This exam consists of two parts. The rst part is an in class portion and consists of 5 questions and you will have the duration of the class period to complete it. The second part is a
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 2013 Practice Midterm Exam 1 Solutions MATH 3160 - Probability - Fall 2013 Practice Midterm Exam 1 Solutions 1. For each of the following statements, determine whether it is true (T) or false (F): (a) There are 180 dierent arrangements of
School: UConn
Course: Probability
MATH 3160 - Fall 2013 Practice Midterm Exam 1 MATH 3160 - Probability - Fall 2013 Practice Midterm Exam 1 Instructions: Each of the n problems below is worth the same. You MUST answer the T/F questions in Problem 1. For this problem, only the nal answer
School: UConn
Course: Probability
NAME: Spring 2014 18.440 Final Exam: 100 points Carefully and clearly show your work on each problem (without writing anything that is technically not true) and put a box around each of your nal computations. 1. (10 points) Let X be a uniformly distribute
School: UConn
Course: Probability
Spring 2014 18.440 Final Exam Solutions 1. (10 points) Let X be a uniformly distributed random variable on [1, 1]. (a) Compute the variance of X 2 . ANSWER: Var(X 2 ) = E[(X 2 )2 ] E[X 2 ]2 , and 1 (x2 /2)dx = E[X 2 ] = 1 1 E[(X 2 )2 ] = E[X 4 ] = 1 x3 6
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: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 9 MATH 3160 - Probability - Fall 2014 Assignment 9 (Due Wednesday, November 12, at the beginning of class) Relevant sections: Ross, 6.36.7. Please show all work. Justify your numerical answer with brief explan
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 8 MATH 3160 - Probability - Fall 2014 Assignment 8 (Due Wednesday, October 29, at the beginning of class) Relevant sections: Ross, 4.7 (on the Poisson process), 5.5 (skip 5.5.1), 9.1 (a more formal discussion
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 7 MATH 3160 - Probability - Fall 2014 Assignment 7 (Due Wednesday, October 22, at the beginning of class) Relevant sections: Ross, 5.15.4. Problems on the exponential distribution (5.5) are postponed till Assi
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 6 MATH 3160 - Probability - Fall 2014 Assignment 6 (Due Wednesday, October 15, at the beginning of class) Relevant sections: Ross, 4.6 (skip 4.6.2), 4.7 (skip Example 7d and 4.7.1), 4.8 (skip 4.8.4). An indept
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 5 MATH 3160 - Probability - Fall 2014 Assignment 5 (Due Wednesday, October 8, at the beginning of class) Relevant sections: Ross, 4.14.5, 4.94.10. Please show all work. You should EITHER write at least a sente
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 4 MATH 3160 - Probability - Fall 2014 Assignment 4 (Due Wednesday, September 24, at the beginning of class) Relevant sections: Ross, 3.2, 3.3, 3.4 (skip Example 4m1 ), 3.5 (skip Examples 5c, 5e, 5f). . Exam re
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 3 MATH 3160 - Probability - Fall 2014 Assignment 3 (Due Wednesday, September 17, at the beginning of class) Relevant sections: Ross, 2.5 (skip Example 5o), 3.4 (up to Example 4h). Please show all work. You sho
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 2 MATH 3160 - Probability - Fall 2014 Assignment 2 (Due Wednesday, September 10, at the beginning of class) Relevant sections: Ross, 2.22.5, up to and including Example 5j. Please show all work. You should EIT
School: UConn
Course: Probability
MATH 3160 - Fall 2013 (J. P. Chen) Final Exam (Version 1B) University of Connecticut MATH 3160 - Probability - Fall 2013 Final Exam (Version 1B) Name: I hereby agree that I shall not communicate any content of this exam to anyone else, until after the end
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 1 MATH 3160 - Probability - Fall 2014 Assignment 1 (Due Wednesday, September 3, at the beginning of class) Relevant sections: Ross, 1.11.5. (1.6 is optional reading.) Ground rules on homework assignments: Plea
School: UConn
Course: Probability
MATH 3160 - Fall 2013 (J. P. Chen) Final Exam Solutions MATH 3160 - Probability - Fall 2013 Final Exam Solutions 1. This problem is best attacked by drawing a Venn diagram. Let A be the set of respondents who like Kim, and B be the set of respondents who
School: UConn
Course: Probability
MATH 3160 - Fall 2013 (J. P. Chen) Midterm Exam 1 University of Connecticut MATH 3160 - Probability - Fall 2013 Midterm Exam 1 (October 2, 2013) Name: Section (circle one): Problem 001 004 Score 1 2 3 4 5 6 Total . Instructions: Each of the 6 problems in
School: UConn
Course: Probability
MATH 3160 - Fall 2013 Midterm Exam 1 Solutions MATH 3160 - Probability - Fall 2013 Midterm Exam 1 Solutions 1. For each of the following statements, determine whether it is true (T) or false (F): (a) There are 60 dierent arrangements of the letters UCONN.
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: Geometry
MATH 2360Q UNIVERSITY OF CONNECTICUT SPRING 2014 MIDTERM EXAM 2 Name: This exam consists of two parts. The rst part is an in class portion and consists of 6 questions and you will have the duration of the class period to complete it. The second part is a
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 6 SOLUTIONS 1. Exercise 7.1.3 Prove that ABCD is a convex set according to Denition 3.3.1 whenever convex quadrilateral according to Denition 4.6.2. Proof: Let ABCD is a ABCD be a convex quadrilateral. By Denit
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 7 SOLUTIONS 1. Exercise 8.1.6 Let = C(O, r) be a circle, let and m be two nonparallel lines that are tangent to at the points P and Q, and let A be the point of intersection of and m. Prove the following (in ne
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 5 SOLUTIONS 1. Exercise 5.1.6 Prove that the angles in a triangle measure 45 , 45 , and 90 if and only if the triangle is both right and isoceles. Proof: Let ABC be such that (ABC) = (BAC) = 45 and (ACB) = 90 .
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 4 SOLUTIONS 1. Exercise 4.5.2 Corollary 4.5.7 Let and be two lines cut by a transversal t. If and meet on one side of t, then the sum of the measures of the two interior angles on that side of t is strictly les
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
Generated by CamScanner Generated by CamScanner Generated by CamScanner
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: 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
Ch. 6 Applications of Integration 6.2 Volumes In this section we will learn how to use integrals to compute the volume of threedimensional solids. In doing so we will use two methodsthe method of disks and the method of washers. We begin with some simple
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.1 Integration by Parts In this chapter we will examine various techniques for evaluating integrals. We begin this section with a review all of the integration formulas we have studied as well as a brief review of the one
School: UConn
Course: CALCULUS II
Ch. 6 Applications of Integration 6.1 Areas Between Curves In a previous section we defined the area under the curve y = f (x) as the limit of the n Riemann sums, that is, A = lim f ( x *i )x . Next we defined the Definite Integral of n i =1 b f from a
School: UConn
Course: CALCULUS II
Chapter 9Differential Equations 9.1Modeling With Differential Equations Similar to what we studied in section 9.1, in this section we will examine DE that are used to model population growth including, the law of natural growth, the logistic equation, an
School: UConn
Course: CALCULUS II
11.4 The Comparison Tests In using the Comparison Tests to test for convergence or divergence we will compare a given series with a series that we know to be either convergent or divergent. For example, suppose we wanted to test whether the series is co
School: UConn
Course: CALCULUS II
University of Connecticut Department of Mathematics Math 1132 Practice Exam 1 Spring 2014 Name: Instructor Name: TA Name: Section: Discussion Section: Read This First! Please read each question carefully. Show ALL work clearly in the space provided. In o
School: UConn
Course: CALCULUS II
Let y(t) be the amount of alcohol in the vat after t minutes. Now, y(0) = (0.04)(500)= 20 gals, so initially the vat with 500 gals of beer contains 20 gals of alcohol. Now the amount of beer at all times in the vat remains at 500 gals so the %-age of alco
School: UConn
Course: CALCULUS II
Math 1132 Practice Final Exam Important Notice: To prepare for the nal exam, one should study the past exams and practice midterms (and homeworks, quizzes, and worksheets), not just this practice nal. A topic not being on the practice nal does not mean it
School: UConn
Course: Mathematics For Business And Economics
Exam 1 Extra Practice Problems Math 1071Q Spring 2013 1. Find the domain of each of the following functions: (a) f (x) = 2x3 + 7x 5 (b) g(x) = x + 1 (c) h(x) = (d) k(x) = x2 +1 x2 1 3x x2 (e) j(x) = ln(2x + 3) 2. Solve the following equations for x: (a) 1
School: UConn
Course: Mathematics For Business And Economics
Math1071Q Fall 2013 Exam 2 review sheet 1. Find d (f (x) dx i f (x) = where 2 xix f (x) = ii f (x) = x1.4 xx f (x) = e3x (without using the chain rule) iii f (x) = 4 x x2 xxi f (x) = e3x (this time using the chain rule) iv f (x) = 1 ex 3 v f (x) = 4 3 ln
School: UConn
Course: Mathematics For Business And Economics
MATH 1071Q Fall 2013 Final Review 1. Dierentiate (a) F (x) = (4x3 + 5)2 (x4 2x)3 (b) H(z) = ln |3z 6 4z + 10| (c) S(x) = ln |x(x 4)| (d) y = e5x (x3 8x+5) 2. Evaluate (a) (b) (x3 5 x + 8)dx (x4 2x3 ) dx x (c) (9x 13)12 dx (d) xe(x 2 +1) dx 3. Find g(x) g
School: UConn
Course: Calculus 1
Math 1125Q Exam 1 Review Name: June 28, 2012 1. Find the domain of the following functions, using interval notation. 1 (a) f (x) = 2x 10 (b) f (x) = x2 16 (c) f (x) = ln(3x 1) x1 (d) f (x) = 2 x 4 2. Given f (x) = x3 1, g(x) = ln(x), h(x) = x nd and simp
School: UConn
Course: Calculus 1
Math 1125Q Exam 2 Review Name: July 5, 2012 1. The position of an object moving along a line is given by the function s(t) = 16t2 + 64t + 100. Find the average velocity of the object over the following intervals (a) [0, 3] (b) [0, 2] (c) [0, 1] (d) [0, h]
School: UConn
Course: Calculus 1
Math 1125Q Exam 2 Review Name: July 12, 2012 1. Find the vertical asymptotes of the following functions 1 (a) f (x) = 2 x 1 x2 + 3x + 2 (b) f (x) = x2 4 (c) f (x) = cot x tan(x) (d) f (x) = sin(x) 2. Find the horizontal asymptotes of the following functio
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: 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: Geometry
MATH 2360Q UNIVERSITY OF CONNECTICUT SPRING 2014 MIDTERM EXAM 1 Name: This exam consists of two parts. The rst part is an in class portion and consists of 5 questions and you will have the duration of the class period to complete it. The second part is a
School: UConn
Course: Probability
MATH 3160 - Fall 2013 Practice Midterm Exam 1 Solutions MATH 3160 - Probability - Fall 2013 Practice Midterm Exam 1 Solutions 1. For each of the following statements, determine whether it is true (T) or false (F): (a) There are 180 dierent arrangements of
School: UConn
Course: Probability
MATH 3160 - Fall 2013 Practice Midterm Exam 1 MATH 3160 - Probability - Fall 2013 Practice Midterm Exam 1 Instructions: Each of the n problems below is worth the same. You MUST answer the T/F questions in Problem 1. For this problem, only the nal answer
School: UConn
Course: Probability
NAME: Spring 2014 18.440 Final Exam: 100 points Carefully and clearly show your work on each problem (without writing anything that is technically not true) and put a box around each of your nal computations. 1. (10 points) Let X be a uniformly distribute
School: UConn
Course: Probability
Spring 2014 18.440 Final Exam Solutions 1. (10 points) Let X be a uniformly distributed random variable on [1, 1]. (a) Compute the variance of X 2 . ANSWER: Var(X 2 ) = E[(X 2 )2 ] E[X 2 ]2 , and 1 (x2 /2)dx = E[X 2 ] = 1 1 E[(X 2 )2 ] = E[X 4 ] = 1 x3 6
School: UConn
Course: Probability
MATH 3160 - Fall 2013 (J. P. Chen) Final Exam (Version 1B) University of Connecticut MATH 3160 - Probability - Fall 2013 Final Exam (Version 1B) Name: I hereby agree that I shall not communicate any content of this exam to anyone else, until after the end
School: UConn
Course: Probability
MATH 3160 - Fall 2013 (J. P. Chen) Final Exam Solutions MATH 3160 - Probability - Fall 2013 Final Exam Solutions 1. This problem is best attacked by drawing a Venn diagram. Let A be the set of respondents who like Kim, and B be the set of respondents who
School: UConn
Course: Probability
MATH 3160 - Fall 2013 (J. P. Chen) Midterm Exam 1 University of Connecticut MATH 3160 - Probability - Fall 2013 Midterm Exam 1 (October 2, 2013) Name: Section (circle one): Problem 001 004 Score 1 2 3 4 5 6 Total . Instructions: Each of the 6 problems in
School: UConn
Course: Probability
MATH 3160 - Fall 2013 Midterm Exam 1 Solutions MATH 3160 - Probability - Fall 2013 Midterm Exam 1 Solutions 1. For each of the following statements, determine whether it is true (T) or false (F): (a) There are 60 dierent arrangements of the letters UCONN.
School: UConn
Course: Geometry
MATH 2360Q UNIVERSITY OF CONNECTICUT SPRING 2014 MIDTERM EXAM 2 Name: This exam consists of two parts. The rst part is an in class portion and consists of 6 questions and you will have the duration of the class period to complete it. The second part is a
School: UConn
Course: Calculus II
Math 1132 Solutions to Practice Exam 2 1(a) If the nth partial sum of a series 2n then an = for n > 1 3n an is sn = 1 + n=1 (a) n 3n F Solution: 1 2 3 4 sn = a1 + a2 + a3 + . . . an1 + an = sn1 + an sn = sn1 + an = an = sn sn1 n1 n n1 n an = (1 + n ) (1 +
School: UConn
Course: Calculus II
Math 1132 Practice Exam 2 1. If the statement is always true, circle the printed capital T. If the statement is sometimes false, circle the printed capital F. In each case, write a careful and clear justication or a counterexample. 1 X n (a) If the nth pa
School: UConn
Course: Calculus II
University of Connecticut Department of Mathematics Math 1132 Practice Exam 1 Solutions Spring 2014 Name: Instructor Name: Section: TA Name: Discussion Section: Read This First! Please read each question carefully. Show ALL work clearly in the space prov
School: UConn
Course: Calculus II
University of Connecticut Department of Mathematics Math 1132 Practice Exam 1 Spring 2014 Name: Instructor Name: TA Name: Section: Discussion Section: Read This First! Please read each question carefully. Show ALL work clearly in the space provided. In o
School: UConn
Course: Calculus II
Math 1132 Practice Final Exam Important Notice: To prepare for the nal exam, one should study the past exams and practice midterms (and homeworks, quizzes, and worksheets), not just this practice nal. A topic not being on the practice nal does not mean it
School: UConn
Course: Calculus II
Math 1132 Practice Final Exam Solutions Important Notice: To prepare for the nal exam, one should study the past exams and practice midterms (and homeworks, quizzes, and worksheets), not just this practice nal. A topic not being on the practice nal does n
School: UConn
Course: Calculus I
University of Connecticut Department of Mathematics Math 1131 Sample Exam 2 Fall 2013 Name: Instructor Name: Section: TA Name: Discussion Section: This sample exam is just a guide to prepare for the actual exam. Questions on the actual exam may or may not
School: UConn
Course: Calculus I
University of Connecticut Department of Mathematics Math 1131 Sample Final Exam Fall 2013 Name: Instructor Name: Section: TA Name: Discussion Section: Read This First! Please read each question carefully. In order to receive full credit on a problem, sol
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2013 Practice Exam 10 Sept. 2013 Time Limit: 50 Minutes Name: This exam contains 5 pages (including this cover page) and 5 problems. Check to see if any pages are missing. You are required to show your work on each problem on this exam. Poi
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2013 Exam 1 16 Sept. 2013 Time Limit: 50 Minutes Name: This exam contains 6 pages (including this cover page) and 4 problems. Check to see if any pages are missing. You are required to show your work on each problem on this exam. Points 1 4
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2013 Final Exam 9 Dec. 2013 Time Limit: 120 Minutes Name: This exam contains 11 pages (including this cover page) and 5 problems. Check to see if any pages are missing. You are required to show your work on each problem on this exam. Unless
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2013 Practice Final Exam 9 Dec. 2013 Time Limit: 120 Minutes Name: This exam contains 8 pages (including this cover page) and 7 problems. Check to see if any pages are missing. You are required to show your work on each problem on this exam
School: UConn
Course: Math For Business & Economics
Exam Two Review 2 and 10 b corrections on site Z-score and formulas from chapter f on website http:/www.math.uconn.edu/ClassHomePages/Math1070/math1070s14/ - info on rooms Math review 4/16 (TONIGHT) in ITE C80 5-7:30pm Ferrones Advice on exam: practice ex
School: UConn
Course: Probability
University of Connecticut Department of Mathematics University of Connecticut Department of Mathematics Math 3160 Exam 1, Fall 2013 Duration: 50 minutes Name: Section: Question Points 1 10 2 10 3 10 4 10 5 10 6 10 Total: Score 50 1. You should attempt 5 o
School: UConn
Course: Probability
University of Connecticut Department of Mathematics University of Connecticut Department of Mathematics Math 3160 Exam 2, Fall 2013 Duration: 50 minutes Name: Section: Question Points 1 10 2 10 3 10 4 10 5 10 6 10 Total: Score 50 1. You should attempt 5 o
School: UConn
Course: Probability
Math3160 Quiz #2 Question 1 (4 points total) A pair of fair dice is rolled. What is the probability that the second die lands on a higher value than does the rst? Solution: Let E be the event that the second die rolled has a higher number than the rst. Th
School: UConn
Course: Probability
Math3160 Quiz #3 Question 1 (5 points total) Two cards are randomly chosen without replacement from an ordinary deck of 52 cards. Let B be the event that both cards are aces, let As be the event that the ace of spades is chosen, and let A be the event tha
School: UConn
Course: Probability
Math3160 Quiz #4 Question 1 (5 points total) An insurance company writes a policy to the eect that an amount of money A must be paid if some event E occurs within a year. If the company estimates that E will occur within a year with probability p, what sh
School: UConn
Course: Probability
Math3160 Quiz #6 Question (10 points total) The density function of X is given by f (x) = a + bx2 0 if 0 x 1 otherwise. If E[X] = 3 , then nd a and b. 5 Solution: 1 x(a + bx2 ) dx = xf (x) dx = E[X] = So, if E[X] = 3 5, 0 a b + . 2 4 then 3 a b + = 2 4 5
School: UConn
Course: Probability
Math3160 Quiz #1 Question 1 (5 points total) Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take place? Solution: To answer this question we need to count the number of ways that we can choose 2 people from
School: UConn
Course: Probability
Math3160 Quiz #5 Question 1 (10 points total) At time 0, a coin that comes up heads with probability p is ipped and falls to the ground. Suppose it lands on heads. At times chosen according to a Poisson process with rate , the coin is picked up and ipped.
School: UConn
Course: MULTIVARIABLE CALCULUS
Math 2110Q Final Review Name: April 28, 2014 1. Given the points P (2, 0, 6) and Q(2, 8, 5) (a) Find the poosition vector equal to P Q . (b) Find 2 vectors with length 2 parallel to P Q . (c) Find the vector-valued function r(t) of the line segment P Q. 2
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: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 9 MATH 3160 - Probability - Fall 2014 Assignment 9 (Due Wednesday, November 12, at the beginning of class) Relevant sections: Ross, 6.36.7. Please show all work. Justify your numerical answer with brief explan
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 8 MATH 3160 - Probability - Fall 2014 Assignment 8 (Due Wednesday, October 29, at the beginning of class) Relevant sections: Ross, 4.7 (on the Poisson process), 5.5 (skip 5.5.1), 9.1 (a more formal discussion
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 7 MATH 3160 - Probability - Fall 2014 Assignment 7 (Due Wednesday, October 22, at the beginning of class) Relevant sections: Ross, 5.15.4. Problems on the exponential distribution (5.5) are postponed till Assi
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 6 MATH 3160 - Probability - Fall 2014 Assignment 6 (Due Wednesday, October 15, at the beginning of class) Relevant sections: Ross, 4.6 (skip 4.6.2), 4.7 (skip Example 7d and 4.7.1), 4.8 (skip 4.8.4). An indept
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 5 MATH 3160 - Probability - Fall 2014 Assignment 5 (Due Wednesday, October 8, at the beginning of class) Relevant sections: Ross, 4.14.5, 4.94.10. Please show all work. You should EITHER write at least a sente
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 4 MATH 3160 - Probability - Fall 2014 Assignment 4 (Due Wednesday, September 24, at the beginning of class) Relevant sections: Ross, 3.2, 3.3, 3.4 (skip Example 4m1 ), 3.5 (skip Examples 5c, 5e, 5f). . Exam re
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 3 MATH 3160 - Probability - Fall 2014 Assignment 3 (Due Wednesday, September 17, at the beginning of class) Relevant sections: Ross, 2.5 (skip Example 5o), 3.4 (up to Example 4h). Please show all work. You sho
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 2 MATH 3160 - Probability - Fall 2014 Assignment 2 (Due Wednesday, September 10, at the beginning of class) Relevant sections: Ross, 2.22.5, up to and including Example 5j. Please show all work. You should EIT
School: UConn
Course: Probability
MATH 3160 - Fall 2014 (J. P. Chen) Assignment 1 MATH 3160 - Probability - Fall 2014 Assignment 1 (Due Wednesday, September 3, at the beginning of class) Relevant sections: Ross, 1.11.5. (1.6 is optional reading.) Ground rules on homework assignments: Plea
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 6 SOLUTIONS 1. Exercise 7.1.3 Prove that ABCD is a convex set according to Denition 3.3.1 whenever convex quadrilateral according to Denition 4.6.2. Proof: Let ABCD is a ABCD be a convex quadrilateral. By Denit
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 7 SOLUTIONS 1. Exercise 8.1.6 Let = C(O, r) be a circle, let and m be two nonparallel lines that are tangent to at the points P and Q, and let A be the point of intersection of and m. Prove the following (in ne
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 5 SOLUTIONS 1. Exercise 5.1.6 Prove that the angles in a triangle measure 45 , 45 , and 90 if and only if the triangle is both right and isoceles. Proof: Let ABC be such that (ABC) = (BAC) = 45 and (ACB) = 90 .
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 4 SOLUTIONS 1. Exercise 4.5.2 Corollary 4.5.7 Let and be two lines cut by a transversal t. If and meet on one side of t, then the sum of the measures of the two interior angles on that side of t is strictly les
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 PROBLEM SET 3 SOLUTIONS 1. Exercise 4.2.1 Theorem 4.2.2 If ABC is a triangle such that ABC ACB, then AB AC. = = Proof: Let ABC be a triangle with ABC ACB (hypothesis). Then by ASA and the = CB, ABC ACB. By denition of con
School: UConn
Course: Geometry
SPRING 2014 MATH 2360Q SECTION 3 EXTRA CREDIT PROBLEM SET SOLUTIONS 1. Exercise 6.4.1 Prove that if Q P D and QD|AB, then P D|AB. Proof: Let Q P D and QD|AB. Assume to the contrary that there exists an F such that P F is between P A and
School: UConn
Course: Calculus II
Math 1132 Worksheet 6 Due: FIRST discussion section in the week of April 7th Innite Series II Solutions to these problems should include your work. Part 1: Convergence of Series. 1. Let s = n=1 (1)n1 . 3n + 2 (a) Write out the rst 5 terms in this series,
School: UConn
Course: Calculus II
Math 1132 Worksheet 7 Due: 1st discussion section in the week of April 28th Parametric Curves Part 1: Parametrizations. 1. In each part of this problem, (i) eliminate the parameter to obtain an equation in terms of x and y, (ii) graph the parametric curve
School: UConn
Course: Calculus II
Math 1132 Worksheet 5 Due: 2nd discussion section in the week of March 26th Innite Series I Solutions to these problems should include your work. Part 1: Sequences and Partial Sums. (1)n1 . n (a) Plot an vs. n for n = 1, 2, 3, 4, 5, 6, 7, 8. 1. Let an = a
School: UConn
Course: Calculus II
Math 1132 Worksheet 2 Due: 2nd discussion section in the week of Feb. 3rd Area between Curves, Volumes, and Work (0, 8) Solutions to these problems should show all of your work, not just a single nal answer. All areas are nice numbers, not nasty decimals.
School: UConn
Course: Calculus II
Math 1132 Worksheet 4 Due: 2nd discussion section in the week of Mar. 3rd Applications of Integration Part 1: Hydrostatic Force. 1. The wall of a dam is an isosceles trapezoid, measuring 80 meters on the bottom, 40 meters on the top, and being 30 meters t
School: UConn
Course: Calculus II
Math 1132 Worksheet 3 Due: 2nd discussion section in the week of Feb. 17th Methods of Integration Solutions to these problems should show all of your work, not just a single nal answer. Part 1: Integration by parts. Do each problem as follows: (1) specify
School: UConn
Course: Calculus II
Math 1132 Worksheet 1 Due: 1st discussion section in the week of Jan. 27th Integration by Substitution (Review) Part 1: Compute the indenite integral in three steps: (1) specify the substitution u =? and du =?, (2) rewrite the integral completely in terms
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
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 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
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
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 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: Actuarial Mathematics I
Math 3630 Fall 2014 Homework Assignment 2 Due Date: Wednesday 24 September, 12:00 pm, 404 MSB (because of the career fair) General Notes: Please hand in Part I on paper, at the beginning of class on the due date. In order to get full credit, you must sho
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2014 Homework Assignment 2 Due Date: Wednesday 24 September, 12:00 pm, 404 MSB (because of the career fair) General Notes: Please hand in Part I on paper, at the beginning of class on the due date. In order to get full credit, you must sho
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2014 Homework Assignment 1 Due: September 16th at 2:00 pm General Notes: Your answers should consist entirely of your own work; you must NOT copy from any other source or person. 1. Jimmy recently purchased a house for he and his family to
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2014 Homework Assignment 3 Due Date: Oct 16, 2:00 pm General Notes: Please hand in Part I on paper, by 2:00 pm on the due date to the box outside my oce (MSB 404). In order to get full credit, you must show ALL work. For Part II, you shou
School: UConn
Course: Actuarial Mathematics I
Assignment to Sell Insurance (revised 4/11/2014) Note: This document and assignment were adapted with permission from Ron Gebhardtsbauer, FSA, MAAA. Thanks to Prof. Gebhardtsbauer of Penn State University for providing this idea and for helpful conversati
School: UConn
Course: Actuarial Mathematics I
Subpart A y=82 *Note: All Final Answers are Highlighted in Green A) 1 Age of Death PV of Payment A) 2 82 Err:510 83 Err:510 84 Err:510 85 Err:510 86 Err:510 87 Err:510 88 Err:510 89 Err:510 90 Err:510 91 Err:510 92 Err:510 93 Err:510 94 Err:510 95 Err:510
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2014 Homework Assignment 3 Due Date: Oct 16, 2:00 pm General Notes: Please hand in Part I on paper, by 2:00 pm on the due date to the box outside my oce (MSB 404). In order to get full credit, you must show ALL work. For Part II, you shou
School: UConn
Course: Actuarial Mathematics I
Math 3630 Fall 2014 Homework Assignment 4 Due Date: Thursday November 6 General Notes: Please hand in Part I on paper, by 2:00 pm on the due date to the box outside my oce (MSB 404). In order to get full credit, you must show ALL work. For Part II, you
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 Homework Assignment 4 Due Date: Thursday November 6 General Notes: Please hand in Part I on paper, by 2:00 pm on the due date to the box outside my oce (MSB 404). In order to get full credit, you must show ALL work. For Part II, you
School: UConn
Course: Probability
Math3160 Worksheet #1 1. Some simple combinatorial problems to get us started: (a) In how many ways can 3 boys and 3 girls sit in a row? (b) In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together? (c) In ho
School: UConn
Course: Probability
Math3160 Worksheet #2 1. Suppose I have 4 people who are going to spend the night at a hotel in two rooms, with two people in each room. How many ways are there for the people to pair up? 2. Suppose 20 people are gathered together and consist of 10 marrie
School: UConn
Course: Probability
Math3160 Worksheet #3 1. Suppose that it takes at least 9 votes from a 12 member jury to convict a defendant. Suppose also that the probability that a juror votes a guilty person innocent is 0.2, whereas the probability that the juror votes an innocent pe
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: 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