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Unformatted text preview: Stat 150 Midterm, J.P., Spring 2006. Student name in CAPITALS: A. Warmup. Little explanation required. Just apply results from class notes or text. 1. A Poisson( ) number of dice are rolled. Let N i be the number of times face i appears among these dice. Describe the joint distribution of N 1 and N 2 . 2. A random walk starting at 3 moves up 1 at each step with probability 2 / 3 and down 1 with probability 1 / 3. What is the probability that the walk reaches 10 before 0? 3. For the same random walk, what is the expected number of steps until reaching either 0 or 10? 4. Let T r be the number of tosses until the r th H in independent coin tosses with p the probability of H on each toss. Write down the probability generating function of T r . 5. Let U r be the number of tosses until the pattern of HTHT....HT of length 2 r appears (meaning the HT is repeated r times in a row). Give a formula for E ( U r )....
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 Spring '09
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