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John runs an outdoor restaurant. Every day, he is unable to open the restaurant due to bad weather with probability p, independently of all other days. Let Y be the number of consecutive days that John is able to keep the restaurant open between bad weather days. Let X be the total number of customers at the restaurant in this period of Y days. Conditional on Y, the distribution of X is (X |Y) ~ Poisson(μY).
a) What is the distribution of Y and compute the E[Y] and Var[Y].
b) What is the average number of customers at the restaurant between bad weather days?
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