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