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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...
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?
