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.