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Problem 6. Assume that the number of storms N in the upcoming rainy season is random and follows a Poisson distribution, but with a parameter A that is also random and is uniformly distributed on the interval (0,5). That is. Л ~ Unif(0,5). and given that = λ the conditional distribution of N is Poisson with mean λ: a Praioanyno.s) a) Calculate E(N 1 Λ) and E(N). b) Calculate Var(N | Л) and Var(N). c) Find the probability that zero storms occur this season. d) Given that zero storms occur this season, what is the conditional distribution

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