Unformatted text preview: (d) If you win $1 each time head shows up and if you lose 1$ if tail shows up, are you playing a ’fair’ game? Explain your reasoning. Problem 4: (Problem 56, p.175) The number of daily accidents in a certain city is Poisson distributed. On a rainy day the parameter is λ = 0 . 8 and on a dry day it is μ = 0 . 2. Let X denote the number of accidents tomorrow, when it is predicted that it is a rainy day with probability 0 . 6. ±ind (a) E [ X ]. (b) P ( X = 0). (c) V ar ( X ). Problem 5: (Problem 57, p.175) The number of storms in an upcoming season is Poisson distributed with parameter λ which itself is random and has a uniform distribution over the interval (0 , 5). ±ind the probability that there are at least 3 storms this season....
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 Spring '08
 DENKER
 Stochastic Modeling, Probability theory, overall winner

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