Two transmitters send messages through bursts of radio signals to an antenna. During each time slot, each transmitter sends a message with probability p. Simultaneous transmissions result in a loss of the messages. Let X denote the number of time slots until the first message gets through.
(a) Describe the underlying sample space Ģ of this random experiment and specify a Ģ-field and the probabilities of the underlying events.
(b) Show the mapping from Ģ to ĢX, the range of X.
(c) Find the probabilities for the various values of X.