Probability Theory—Homework Assignment #5

Due Tuesday, November 17 at noon (in Joy’s mailbox or under her door)

Honor Code Reminder

There are two types of homework problems: 1) problems on which you are free to work together and 2) work-alone problems. On the work-together problems, your write-up should be your own (you can talk with other students about the problems, but you must write up the solutions individually—that is, you can write scratch work from your study sessions, but you must use your own words and explanations when writing up your final solution). On the work-alone problems, you should not talk with other students at all (except perhaps to clarify what a question is asking)—please see me in office hours with questions about the work-alone problems.

Exposition Reminder

Your grade will depend on both the content and exposition of your answers; write up the problems as carefully as you did—or should have done—in Math 310. That is, be sure your logic is clear, you defend all your steps (unless they are, for example, obvious algebra steps), your solutions read smoothly (even if using symbols—they should still read like an English sentences), and that one of your peers could read and understand your solutions without asking any additional questions.

Okay-to-work-together Problems (4 problems)

Chapter 6 Problems: 27 (hints: use the distribution-function technique to find the pdf of Z; finding the cdf will require integration of the joint pdf; for the second part of the question, use the result from the first part of the problem—it makes life much easier), 30

Chapter 7 Problems: 42 (hint: for each part, create an appropriate indicator variable—as we did in class for problem 34)

Chapter 7 Theoretical Exercises: 49

Work-alone Problems (5 problems)

Chapter 6 Problems: 18

Chapter 6 Theoretical Exercises: 7 (hints: use the distribution-function technique for part a; for part b, explicitly use the result in part a—it makes life much easier)

Chapter 7 Problems: 75

Chapter 7 Theoretical Exercises: 13, 51 (the book says “Use Table 7.2”; what this means is “carefully use the moment-generating-function technique to show the result”)