In a wireless automatic meter reading system, a base station sends out a wake-up signal to nearby electric meters. On hearing the wake-up signal, a meter transmits a message indicating the electric usage. Each message is repeated eight times.
(a) If a single transmission of a message is successful with probability p, what is the PMF of N, the number of successful message transmissions?
(b) I is an indicator random variable such that I = 1 if at least one message is transmitted successfully; otherwise I = 0. Find the PMF of I.