Math 431 – Spring 2013
Homework 8
Due: April 18, 2013, by 10 a.m. (in class the day before, in my office, or under
my door, NOT in my mailbox).
Please read the instructions/suggestions written in the syllabus!
• Hand in the following problems:
1. Problems from Pitman:
–
–
–
–
4.5:
5.1:
5.2:
5.4:
6
4, 8
4, 7, 16
1, 13
Hints:
5.1.8: transform the event so that it is about the original random variables (not the
ordered ones)
5.2.16: this is similar to Example 2 in the book, but now you have a triple integral
to compute.
5.4.13: consider the random variable Ỹ = −Y , then X − Y = X + Ỹ .
2. Find the density of X + Y when X and Y are independent and exponentially
distributed with distinct parameters λ 6= µ.
• Practice problems from textbook (you do not need to hand these in!):
4.5: 1-8 (harder: 9),
Ch 4: Review: 1-16, 18-19, 21-26 (harder: 27-30)
5.1: 1-8 (harder: 9)
5.2: 1-5, 6 a, b, 7, 8 a, b, 9, 11, 12, 13, 16 (harder: 10, 14-15, 17-20)
5.4: 1-4, 6, 13, (harder: 5, 7-12, 14-15, 19)
• Bonus problem:
5.2.10 from the book.
Disclaimer: It is easy to find the solutions to (some of) these questions. (E.g. the internet,
your fellow classmates . . . ) However, do NOT consult any of these solutions when working on
this assignment or you will learn nothing from it and your chance of passing the course will
be greatly diminished. If it becomes apparent to the grader that your solution is copied from
existing solutions, you will be assigned a grade of zero for lack of originality.