Stochastics: HW 7, due Wed Apr 23

1. The Autocovariance problem posted last week.. 2. Consider the random variable and let be the event that or . Compute . Compute . Let be distributed like and let .  Compute . Compute . 3. Let be a sequence of iid random variables and let .  Let be the moment generating function of (andContinue reading “Stochastics: HW 7, due Wed Apr 23”

Stochastics: HW 6, due Wed April 16

Durrett 3.8 Counter processes. Suppose that arrivals at a counter come at times of a Poisson process with rate .  An arriving particle that finds the counter free gets registered and then locks the counter for an amount of time . Particles that arrive while the counter is locked are not counted and have no effect.Continue reading “Stochastics: HW 6, due Wed April 16”

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 areContinue reading “Stochastics: HW 5, due Wed April 2”

Stochastics: Suggested Problems for Exam 1

Getting things kicked off on the new website. Here is a list of interesting problems to try from Durrett’s book.  Please use the comments feature to ask questions and to start discussions about these problems. I’ll chime in whenever I can. Stationary distributions and limit distributions 1.20, 1.25, 1.38, 1.41, 1.44 Random walks on graphsContinue reading “Stochastics: Suggested Problems for Exam 1”