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12. People arrive at a shoe store at random. Each person then looks at a random number of shoes
deciding which to buy.
(a) Let N be the number of people that arrive in an hour. Given that EN = 10, what wou
good distribution for N?
(b) Customer i tries on X, pairs of shoes they do not like before finding a pair they like an
purchase (X, ( {0, 1,...}). Suppose that the chance they like a given pair of shoes in 0.
pendently of the other shoes they have looked at. What is the distribution of X;?
(c) Let Y be the total number of shoes that have been tried on, excluding those purchased. Su

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