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