Question

a) In a multi-user wireless network, the data frames are being transmitted when the probability of collision during the transmission is 0.75. The transmitters try to send the collision-free frames using up to 6 independent trials (transmission) as needed. The transmitters indefinitely discard the data frames after 6 failures. Calculate the probability that a data frame can be successfully transmitted (not be discarded). Let ? denote the random number of trials until the frame is transmitted without collision, find P(X ≤ 5).

b) In the multi-user wireless network, what is the probability that from 5 independent messages sent to a transmitter in the network, 4 or more frames are being successfully (collision-free) sent? Let ? denote the number successfully transmitted frames out of 5 frames, find P(Y ≥ 4).

Answer 1