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Unformatted text preview: Math 452/550: Stochastic processes Homework assignment # 1 Due September 24th, 2010 Submit all of your work for marking. You are permitted to collaborate on the homework; however, you must write up your homework yourself. You should not copy somebody elses homework: if you choose to collaborate, you should be able to recreate all of the steps involved in solving a problem yourself, and should do so in your writeup. Please list the names of your collaborators on the first page of each homework. Assignments must be submitted by the given due date. No late homework will be accepted. 1. i) Compute the moment generating function ( t ) E [ e tX ] of a. a Poisson distribution with mean b. an exponential distribution with parameter > c. a gamma distribution with parameters 1 , > 0. ii) Use these results in i) to show that the sum of two independent Poisson distributions with means 1 , 2 is a Poisson distribution with mean 1 + 2 and that the sum of n independent exponential...
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