Consider two wireless transmitters, a and b, that are near each other. in each time slot, each transmitter sends a message with probability 1/2 and is otherwise idle. whether or not b transmits in a time slot is independent of whether a transmits in the slot. simultaneous transmissions result iin loss of the messages (called a collision). let x be the number of time slots until the first message gets through. (a) describe the underlying sample space 2 of this random experiment and specify the probabilities of its elementary events. (b) find the pmf of x.

in problem 2, suppose that a transmits with probability 1/2 in a given slot, but b transmits with probability p. (a) find the pmf for the number of transmissions x until a message gets through (b) given a successful transmission, find the probability that it was b that transmitted.