homework2_452f10 - Math 452/550: Stochastic processes...

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Math 452/550: Stochastic processes Homework assignment # 2 Due In Class, Oct. 8th, 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 else’s 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. Show that the product of two stochastic matrices is a stochastic matrix. 2. Consider a Markov chain with three states 0,1,2 and a transition probability matrix P = 1 / 2 1 / 3 1 / 6 0 1 / 3 2 / 3 1 / 2 0 1 / 2 . Find E [ X 4 ] if P { X 0 = i } = 1 / 3 ,i = 0 , 1 , 2. 3. Let ( X n ) n 0 be a Markov chain with the probability transition matrix P = ( p ij ) i,j 0 on the discrete states 0,1,2,
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homework2_452f10 - Math 452/550: Stochastic processes...

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