This problem set is due on Thursday 2/21.

You may consult whoever and whatever you like, but be sure to list your collaborators, write up your solutions in your own words without referring to any notes you might have jotted down from the consultation, and be ready to solve similar problems from scratch.

In addition to the following exercises, please do problems 5, 7, 12, 13, 15, 18, 23, and 25 from Bertsekas and Tsitsiklis’s Chapter 1. In problem 13, give the answer as a fraction. In problem 18, a recursive formula is a recursive function that takes m and n as its two arguments.

1. Write a program using a random number generator to perform the experiment described in problem 7 from Bertsekas and Tsitsiklis’s Chapter 1. The program should return a representation of the sample obtained; describe the format of this representation in English.

2. Prove from the probability axioms that P(A^c) = 1 − P(A) and P(A) = P(A ∩ B) + P(A ∩ B^c).