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STA 4321  Intro To Probability  University Of Florida Study Resources

ISM_chapter4
School: University Of Florida
Course: INTRO TO PROBABILITY
Chapter 4: Continuous Variables and Their Probability Distributions y <1 0 .4 1 y < 2 a. F ( y ) = P(Y y ) = .7 2 y < 3 .9 3 y < 4 1 y4 1.0 F(y) 0.0 0 0.2 0.4 0.6 0.8 4.1 1 2 y 3 4 5 b. The graph is above. 4.2 a. p(1) = .2, p(2) = (1/

ISM_chapter10
School: University Of Florida
Course: INTRO TO PROBABILITY
Chapter 10: Hypothesis Testing 10.1 10.2 See Definition 10.1. Note that Y is binomial with parameters n = 20 and p. a. If the experimenter concludes that less than 80% of insomniacs respond to the drug when actually the drug induces sleep in 80% of i

Annual97
School: University Of Florida
Course: Introduction To Probability
Annual Report March 16, 1996  March 15, 1997 Department of Statistics University of Florida Gainesville, FL 326118545 June, 1997 Contents 1 Research Activities: March 16, 1996  March 15, 1997 7 2 NonRefereed Publications 13 3 Technical Reports 16 4 Gr

ISM_chapter3
School: University Of Florida
Course: INTRO TO PROBABILITY
Chapter 3: Discrete Random Variables and Their Probability Distributions 3.1 3.2 P(Y = 0) = P(no impurities) = .2, P(Y = 1) = P(exactly one impurity) = .7, P(Y = 2) = .1. We know that P(HH) = P(TT) = P(HT) = P(TH) = 0.25. So, P(Y = 1) = .5, P(Y = 1)

ISM_chapter7
School: University Of Florida
Course: INTRO TO PROBABILITY
Chapter 7: Sampling Distributions and the Central Limit Theorem 7.1 a. c. Answers vary. d. The histogram exhibits a mound shape. The sample mean should be close to 3.5 = e. The standard deviation should be close to / 3 = 1.708/ 3 = .9860. f. Very s

Ltrnotes12
School: University Of Florida

Ltrnotes13
School: University Of Florida

Ltrnotes14
School: University Of Florida

Ltrnotes15
School: University Of Florida

Ltrnotes16
School: University Of Florida

Syllabus
School: University Of Florida
STA 4321/5325 Introduction to Probability/Fundamentals of Probability Section 1192 & 6790 Spring 2012 Course Information and Policies Objectives: The sequence of courses STA 43214322 (rep. 53255328) provides a formal and systematic introduction to mathe

Exam1solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability
STA 4321/5325  Spring 2010 Exam 1 February 3, 2010 Full Name: KEY On my honor, I have neither given nor received unauthorized aid on this examination. Signature: This is a 50 minute exam. There are 4 problems, worth a total of 40 points. You may use on

Exam3solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability
STA 4321/5325  Spring 2010 Exam 3 March 29, 2010 Full Name: KEY On my honor, I have neither given nor received unauthorized aid on this examination. Signature: This is a 50 minute exam. There are 4 problems, worth a total of 40 points. You may use one

Ltrnotes11
School: University Of Florida

Ltrnotes10
School: University Of Florida

Lecture9
School: University Of Florida

Hwk7
School: University Of Florida
Solutions to Homework 7 5.140 For gamma distribution with parameters and , the moment generating function is M (t ) etx 0 1 x 1e x / dx ( ) 1 ( ) 0 x 1 x /( e 1 t ) dx ( ) 1 t ( ) 1 t 6.1 a. Let Z denote the number of contracts assigned to firm

Hwk8
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Hwk9
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Lecture 2
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Lecture3
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Lecture4
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Lecture5
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Lecture6
School: University Of Florida

Lecture7
School: University Of Florida

Lecture8
School: University Of Florida

Exam4solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability
STA 4321/5325  Spring 2010 Exam 4 April 19, 2010 Full Name: KEY On my honor, I have neither given nor received unauthorized aid on this examination. Signature: This is a 50 minute exam. There are 4 problems, worth a total of 40 points. You may use one

Quiz1solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Sample Space, Events, And Probability
School: University Of Florida
Course: Intro To Probability Theory
Lecture 2 Agenda 1. Sample Spaces and Events 2. Probability Sample Spaces and Events Whenever we perform any experiment it can result in several dierent outcomes. But before we perform the experiment we cant exactly say which outcome will occur. Denition

Probability, Counting, And Permutations
School: University Of Florida
Course: Intro To Probability Theory
Lecture 3 Agenda 1. One more example to understand the formal denition of probability 2. Fundamental principles of counting 3. Evaluating probabilities using permutations Example Experiment: There are 3 mail boxes. Three people come one after another, and

More Counting
School: University Of Florida
Course: Intro To Probability Theory
Lecture 4 Agenda 1. Some more counting rules 2. And the related examples Remember the following two results from previous lecture. Lemma 1. Total number of ways of selecing r objects from n objects where  order of selection is important &  the same obje

Conditional Probability, Total Probability, And Bayes Rule
School: University Of Florida
Course: Intro To Probability Theory
Lecture 5 Agenda 1. Conditional Probability 2. Theorem of Total probability 3. Bayes Rule Conditional Probability Suppose you are going to have a surgery, but before that you want to talk to a Doctor about how likely it is that the surgery will be a succe

Independence
School: University Of Florida
Course: Intro To Probability Theory
Lecture 6 Agenda 1. Independence Independence In our everyday lives when we see two things which are not inuenced by one another, we call them independent of each other. For example how many sandwitches you will eat today and whether the Gators are gonna

Inclusion Exclusion Principle, Random Variable, And Discrete Random Variable
School: University Of Florida
Course: Intro To Probability Theory
Lecture 7 Agenda 1. Inclusion Exclusion Principle 2. Random Variable 3. Discrete Random Variable Inclusion Exclusion Principle Theorem 1. If A1 , A2 , . . . , Ak are k events, then k P (A1 A2 . . . Ak ) = P (Ai ) P (Ai1 Ai2 ) + 1i1 <i2 n i=1 (k1) . . . .

More Discrete Random Variable, Pmf, Pdf
School: University Of Florida
Course: Intro To Probability Theory
Lecture 8 Agenda 1. Discrete Random Variable from previous class completed 2. Probability mass function 3. Probability distribution function Probability mass function Let X be a discrete random variable. Hence Range(X ) is a countable set and thus it can

Properties Of Distribution Functions, Expectation
School: University Of Florida
Course: Intro To Probability Theory
Lecture 9 Agenda 1. Properties of distribution function 2. Expectation Properties of distribution function Let X be a random variable. Then its probability distribution function FX (b) is dened as FX (b) = P (X b) for b R. Properties 1. lim FX (x) = 0 x 2

Properties Of Expectation, Random Variable Expectation
School: University Of Florida
Course: Intro To Probability Theory
Lecture 10 Agenda 1. Examples involving expectation of a random variable 2. Properties of Expectation Examples involving expectation of a random variable Example 1 Roll a fair die twice. Let X denote the sum of the two outcomes. Lets nd the expectation of

Samplefinalexamsolns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Sampleexam4solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability
STA 4321/5325  Spring 2010 Sample Exam 4 Note: This is an example adapted from previous STA 4321/5325 exams. It is intended to be of approximately the same length and style as the actual exam. However, it is NOT guaranteed to match the content or coverag

Quiz7solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Quiz2solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Quiz3solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Quiz4solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Quiz5solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Quiz6solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Quiz8solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability

Quiz9solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability
STA 4321/5325  Spring 2010 Quiz 9  April 16 Name: There are ve problems in this quiz. Each problem has exactly one correct answer. Problem 1 Let X and Y be independent random variables with E (X ) = 2, E (Y ) = 1, V (X ) = 16, and V (Y ) = 3. Then (a) E

Sampleexam3solns
School: University Of Florida
Course: Introduction To Probability / Fundamentals Of Probability
STA 4321/5325  Spring 2010 Sample Exam 3 Note: This is an example adapted from previous STA 4321/5325 exams. It is intended to be of approximately the same length and style as the actual exam. However, it is NOT guaranteed to match the content or coverag

Variance And Standard Deviation, Indicator Function, Markov And Chebyshev
School: University Of Florida
Course: Intro To Probability Theory
Lecture 11 Agenda 1. Variance and Standard Deviation 2. Indicator Function 3. Markov Inequality and Chebyshevs inequality Variance and Standard Deviation Consider two students and their scores on 4 exams. Tom 49 51 48 Harry 20 80 30 52 70 Both have mean s

Hwk6
School: University Of Florida
Solutions to Homework 6 5.63 Solve equation 0.5 F m 1 e m We get m ln 2 0.693 5.65 Let X denote the daily rainfall during a randomly selected September day. a. E X 8, b. 1 V X 2 160 1 0.75 , then we have k 2 . From Tchebysheffs Theorem, k2 1 P ( X 2 )

Exam3smplf99
School: University Of Florida
Course: Introduction To Probability
Sample Problems for Exam 3 STA 4321 Mathematical Statistics I Fall 1999 These questions are only meant as a study aid and to help you test your knowledge. Being able to solve them does not guarantee that you are wellprepared for the exam. 1. For each of

STA4321ln2
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STA4321ln3
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STA4321ln4
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STA4321ln5
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STA4321ln7
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STA4321ln8
School: University Of Florida

Syllabus43215325Fall06
School: University Of Florida
Course: Introduction To Probability
Fundamentals of Probability STA 4321 (Section 4529) and STAT 5325 (Section 5566) Fall, 2006 Objective: This course is a broad introduction to the mathematical theory of probability. The objective of the course is to introduce the student to probability as

STA4321ln9
School: University Of Florida

STA4321grdcutoffs
School: University Of Florida
These are tentative grade cutoffs, which may be slightly modified later. A = 90 or above A = 8689 B+ = 8185 B = 7180 B = 6670 C+ =6165 C = 5660 C =5155 D+ =4650 D = 4145 D = 3640 E = 35 or below

Courseinfo
School: University Of Florida
STA 4321/5325 Introduction to Probability / Fundamentals of Probability Section 7461/7490 (3 credit hours) Spring 2012 Course Information and Policies Objectives: The sequence of courses STA 43214322 (rep. 53255328) provides a formal and systematic intr

STA4321 HW3(2)
School: University Of Florida
Course: Introduction To Probability
STA 4321 Introduction to Probability Theory Assignment 3 Assigned Friday February 12 Due Monday February 22 Show your work to receive full credit. 1. A study is to be conducted in a hospital to determine the attitudes of nurses toward various administrati

STA4321HW1
School: University Of Florida
Course: Introduction To Probability
STA 4321 Introduction to Probability Theory Assignment 1 Assigned Wednesday January 13 Due Wednesday January 20 Show your work to receive full credit. 1. Let A1 , A2 , . . . be a countable collection of sets. Give a formal proof (not a picture) of the fol

STA4321HW2
School: University Of Florida
Course: Introduction To Probability
STA 4321 Introduction to Probability Theory Assignment 2 Assigned Wednesday January 20 Due Monday January 25 Show your work to receive full credit. 1. Students attending the University of Florida can select from 130 major areas of study. A students major

STA4321HW4
School: University Of Florida
Course: Introduction To Probability
STA 4321 Introduction to Probability Theory Assignment 4 Assigned Monday March 15 Due Monday March 22 Show your work to receive full credit. 1. A machine for lling cereal boxes has a standard deviation of 1 ounce in ll per box. Assume that the ounces of l

Homework1_sol
School: University Of Florida
Course: Introduction To Probability
STA 4321 Solution to Homework 1 2.10 a. Because the two jobs are indentical, the order is not important in this problem. The sample space is S = cfw_J, D, cfw_J, M , cfw_J, S , cfw_J, N , cfw_D, M , cfw_D, S , cfw_D, N , cfw_M, S , cfw_M, N , cfw_S, N . E

Syllabus43215325Fall05
School: University Of Florida
Course: Introduction To Probability
Fundamentals of Probability STA 4321 (Section 4529) and STAT 5325 (Section 5566) Fall, 2005 Objective: This course is a broad introduction to the mathematical theory of probability. The objective of the course is to introduce the student to probability as

Syllabus4322
School: University Of Florida
Course: Introduction To Probability
STA4322 (Sect 5238) Introduction to Statistical Theory STA5328 (Sect 4048)Fundamentals of Statistical Theory Summer B 2009 Instructor: Mark C. Yang Office: 202 GriffinFloyd Hall Phone: 2732979 Email: yang@stat.ufl.edu Office Hours: 5:10pm6:30pm Tuesda

Smplexmstncts
School: University Of Florida

Smplexmstnjtn
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Hwk1
School: University Of Florida
Solutions to Homework 1 2.10 a. The two jobs are identical, so the order does not matter when selecting two applicants, the sample space is S cfw_ Jim, Don , Jim, Mary , Jim, Sue , Jim, Nancy , Don, Mary , Don, Sue , Don, Nancy , Mary, Sue , Mary, Nancy

Hwk2
School: University Of Florida
Solutions to Homework 2 2.41 10 There are ways to choose 4 engineers out of 10, a nd there are 4! ways to assign 4 4 different positions to 4 engineers chosen, thus 10 There are 4! 5040 ways can the director fill the positions. 4 2.50 For each of the 10

Hwk3
School: University Of Florida
4.5 We need to assume each outcome is equally likely for each person to choose each door. Each person has four choices, thus there are 43 64 possible outcomes for three 3 people to enter the building. If x people choose door I, there are ways to specify

Correction For Homework 2
School: University Of Florida
Correction for e of 2.60 : The correct answer should be P (straight) = 10 (45 4) 52 5 which is the same as Prof. Han said in class. My answer to b of 2.60 is correct. There indeed 9 ways to select a straight ush in a specic suit, for 10, J, Q, K, ace in o

Explanations And Correction To Homework 3
School: University Of Florida
Explanation to 3.17 It seems that there are two dierent understandings on eldest daughters. If eldest daughter include the only daughter in the family, the answer is 0.75. The sample space is cfw_B11 B12, B21, B22, G11, G12, G21, G22. B or G denote the ge

Homework1_sol
School: University Of Florida
STA 4321 Solution to Homework 1 2.10 a. Because the two jobs are indentical, the order is not important in this problem. The sample space is S = cfw_J, D, cfw_J, M , cfw_J, S , cfw_J, N , cfw_D, M , cfw_D, S , cfw_D, N , cfw_M, S , cfw_M, N , cfw_S, N . E

Homework2_sol
School: University Of Florida

Homework3_sol
School: University Of Florida

Hwk4
School: University Of Florida
4.51 a. each individual has the probability of 0.5 to pass the gene to an offspring. P ( the child has no disease gene) P (the first person do not pass gene to the child) P (the second person do not pass gene to the child) 0.5 0.5 0.25 b. for each chil

STA4321samplequiz5
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Quiz9
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Exam1solutionSPRING12
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Smlexamstn
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STA4321samplequiz3
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Exam2
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Exam2solutionSPRING10
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Exam3
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Exam4solutionSPRING12
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Quiz3
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Quiz7
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Hwk5
School: University Of Florida
Solutions to Homework 5 5.5 a. 0 0 f x dx ce x /10 dx 10 ce x /10 thus c 10c 1 1 . 10 b. if b 0, F (b) 0 , if b 0, then F (b) b b 1 x /10 e dx e x /10 1 e b /10 0 0 10 f ( x)dx b thus 1 e b /10 , F (b) 0, b0 b0 c. P ( X 15) 1 P( X 15) 1 P( X 15) 1

Final Exam Notes
School: University Of Florida
Course: Intro To Probability
5.2 3 balanced coins are tossed independently. One of the variables of interest is Y1, the number of heads. Let Y2 denote the amount of money won on a side bet in the following manner. If the first head occurs on the first toss, you win $1. If the first h

Lecture8
School: University Of Florida
Course: INTRO TO PROBABILITY
Lecture 8 Zhihua (Sophia) Su University of Florida Jan 26, 2015 STA 4321/5325 Introduction to Probability 1 Agenda Expected Values Variance Properties of Expected Values and Variance Reading assignment: Chapter 3: 3.3, 3.11 STA 4321/5325 Introduction to P

Lecture9
School: University Of Florida
Course: INTRO TO PROBABILITY
Lecture 9 Zhihua (Sophia) Su University of Florida Jan 28, 2015 STA 4321/5325 Introduction to Probability 1 Agenda Tchebyshes Theorem Bernoulli Random Variable Reading assignment: Chapter 3: 3.4, 3.11 STA 4321/5325 Introduction to Probability 2 Tchebyshes

Lecture10
School: University Of Florida
Course: INTRO TO PROBABILITY
Lecture 10 Zhihua (Sophia) Su University of Florida Jan 30, 2015 STA 4321/5325 Introduction to Probability 1 Agenda Binomial Random Variable Geometric Random Variable Reading assignment: Chapter 3: 3.4, 3.5 STA 4321/5325 Introduction to Probability 2 Bino

Lecture11
School: University Of Florida
Course: INTRO TO PROBABILITY
Lecture 11 Zhihua (Sophia) Su University of Florida Feb 2, 2015 STA 4321/5325 Introduction to Probability 1 Agenda Geometric Random Variable Negative Binomial Random Variable Reading assignment: Chapter 3: 3.5, 3.6 STA 4321/5325 Introduction to Probabilit

Lecture12
School: University Of Florida
Course: INTRO TO PROBABILITY
Lecture 12 Zhihua (Sophia) Su University of Florida Feb 4, 2015 STA 4321/5325 Introduction to Probability 1 Agenda Example Poisson Random Variable Reading assignment: Chapter 3: 3.6, 3.8 STA 4321/5325 Introduction to Probability 2 Example Example: A large