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Chapter 3

Required:

I. Complete the following 7 problems:

II. Prove the survival function trick for discrete random variables:

Theorem: Let N be a nonnegative discrete random variable with finite mean. Then E[N]=n=0P(N>n).

Hints:

III. Prove the following property for a discrete random variable X with finite mean.

Theorem: Let X be a random variable with mean E[X], and let a,b be real (non-random) constants. Then E[aX+b]=aE[X]+b.

Hint:

IV. Complete two problems from Problem Solving Session 1 that you did not solve during the problem solving session and that were not presented by the student presenters.