Question

1. A digital data transmission system selects one of the digits 0,1,2, or 3 to transmit through a channel with prior probabilities 0.4, 0.2, 0.2, and 0.2, respectively. The conditional probabilities of receiving the digits 0,1,2 or 3 is transmitted are given in the following table or 3 given that a 0,1,2 P(YreceivedXtransmitted) Xi0 0.95 2 3 0.02 0.02 0.01 1 0.005 0.98 0.005 0.01 2 0.01 0.01 0.97 0.01 3 0.02 0.03 0.02 0.93 Compute the following posterior probabilities: (a) P(X 0|Y 3); (b) P(X = 1|Y 3); (c) P(X 2|Y 3) Comment on the reliability of the channel (i.e., the probabilities of the digits being received соrrectly).

Answer 1

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