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 trans- missions result in loss of the messages. Let X be the number of time slots until the first message gets through.
(a) Find the conditional expected value of X in Problem given that no message gets through in the first time slot. Show that E[X|X>1] = E[X] + 1.
(b) Find the conditional expected value of X in Problem given that a message gets through in the first time slot.
(c) Find E[X] by using the results of parts a and b.
(d) Find E[X2 ]and VAR[X] using the approach in parts b and c.