In a wireless automatic meter reading system, a base
station sends out a wake-up signal to nearby elec-
tric 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 success-
ful 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 success-
fully; otherwise I
= 0. Find the PMF of I