Two transmitters send messages through bursts of radio signals to an antenna. During each time slot each transmitter sends a message with probability 1/2. Simultaneous transmissions result in loss of the messages. Let X be the number of time slots until the first message gets through.

(a) Describe the underlying sample space S of this random experiment and specify the probabilities of its elementary events.

(b) Show the mapping from S to the range of X.

(c) Find the probabilities for the various values of X. Now suppose that terminal 1 transmits with probability 1/2 in a given time slot, but terminal 2 transmits with probability p.

(d) Find the pmf for the number of transmissions X until a message gets through.

(e) Given a successful transmission, find the probability that terminal 2 transmitted.