160a09_quiz2

160a09_quiz2 - Pstat160A Quiz discussion #1 Wednesday,...

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Pstat160A Winter 2009 Quiz discussion #1 Wednesday, March 11 Problem 1: Short questions. 1) Give an application of the reflection principle (just state, no explanations) We found the distribution of the maximum and the number of paths that hit (or doesn’t hit) the x - axis. 2) Can a Markov chain go from a transient class to another transient class? Yes. There are no particular reasons to rule this out. Problem 2: Consider the Markov chain with transition matrix P below. 1. Give the classes, their properties (transience, recurrence) and the period. P = . 4 . 6 0 0 0 . 4 . 6 0 0 0 0 . 6 0 . 4 0 0 0 . 4 0 . 6 0 0 0 1 0 classes: { 1 , 2 } , { 3 , 4 , 5 } property: R, T period: 1 , 2 2. Use the matrices given at the bottom of the page (and P above, to which they relate) to answer the questions below. Also recall the following formulas: f ij = s ij s jj , i 6 = j ; f jj = s jj - 1 s jj a) What is the column of 1.6667 represent in the first matrix below It represents the expected number of steps in 3, starting (respectively) from 3, 4 or 5
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