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People arrive at a queue according to the following scheme: During each minute of time either 0 or 1 person arrives. The probability that 1 person arrives is p and that no person arrives is q = 1 - p. Let Cr be the number of customers arriving in the first r minutes. Consider a Bernoulli trials process with a success if a person arrives in a unit time and failure if no person arrives in a unit time. Let Tr be the number of failures before the rth success.

(a) What is the distribution for Tr ?

(b) What is the distribution for Cr ?

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Statistics and Probability, Statistics

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