A radio program gives concert tickets to the fourth caller with the right answer to a question. Of the people who call, 25% know the answer. Phone calls are independent of one another. The random variable Nr indicates the number of phone calls taken when the rth correct answer arrives.' (If the fourth correct answer arrives on the eighth call, then N4 = 8.)
(a) What is the PMF of N1, the number of phone calls needed to obtain the first correct answer?
(b) What is E[N1], the expected number of phone calls needed to obtain the first correct answer?
(c) What is the PMF of N4, the number of phone calls needed to obtain the fourth correct answer?
(d) What is E[N4]?