Question

In: Statistics and Probability

Two transmitters send messages through bursts of radio signals to an antenna. During each time slot...

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.

Solutions

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Answer:

d)

e)


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