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We monitor the number of incoming calls into a doctor's office. Let X be the number of incoming calls between the hours of l pm and 2 pm and Y be the number of calls between l pm and 3 pm. If we model the number of calls in a period of t hours as a Poisson(lamda(t)) random variable and assume that the number of calls in non-overlapping time periods are independent, show that:

P (X = k | Y = n) = (n k) (1/2) ^n, k = 0,1, ...., n

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