A radio program gives concert tickets to the fourth caller

Question

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 N_r 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].