Stochastics: HW 5, due Wed April 2

This week’s problems are all directly from Durrett:

Chapter 2, #32, 33, 52, 58

Hint: For the chicken crossing the road problem, you may find Theorem 2.10 useful.

UPDATE: It has been brought to my attention that the version of the textbook online has different numbers and one problem is missing altogether. If you are working from the web version, the problem numbers are:

Chapter 2, #33, 34 (chicken crossing the road), 48 (preventative maintenance) and the following,

#58 For a Poisson process $N(t)$ with arrival rate 2, compute: (a) $\mathbb{P}(N(2) = 5)$ , (b) $\mathbb{P}(N(5) = 8 \, | \, N(2) = 3$ , and (c) $\mathbb{P}(N(2) = 3 \, | \, N(5) = 8)$ .