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”

# Category Archives: Stochastics Homework

## 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: Some suggested theoretical exercises

These exercises are not required, but they are recommended for graduate students and others enrolled in the 5000-level of this class. Theoretical Exercises (pdf)

## Stochastics: Suggested Problems for Chapter 2

Practice with exponential random variables 2.1 – 2.3, 2.32 Comparison of multiple exponentially distributed random events 2.7, 2.8 Queueing Theory 2.9, 2.10 The Poisson Process 2.22, 2.23, 2.25, 2.27, 2.33

## Stochastics: HW 4 Solutions

HW 4 (pdf) HW4 Solutions (pdf) In these solutions I reference the use of Wolfram Alpha, (special section on matrix functions here).

## Stochastics: Challenge Problem

If you’re struggling with understanding the notion of detailed balance, try out this quick challenge problem. Consider RW on the graph pictured below. For what value(s) of , does there exist a measure that satisfies the Detailed Balance condition.

## Stochastics: Solutions to HW 3

Note! There was a mistake in the earlier version of these solutions. This version is current as of 5 pm Monday, Feb 24. MAP 4102 Homework 3 (pdf) M4102 HW 3 Solutions (pdf)

## 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”