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 ?
(c) Find the mean and variance for the number of customers arriving in the first r minutes.