In the ternary communication channel shown below, a 3 is sent three times more frequently than a 1, and a 2 is sent two times more frequently than a 1. A 1 is observed; what is the conditional probability that a 1 was sent?

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P[Y=1|X=1]=1-a Y=1 X-1 a/2 a/2 P[Y=2|X=2]=1-B B/2 Y=2 X=2 0. BIZ y/2 X=3 V/2 Y=3 P[Y=3|X=3] = 1-y P[Y=1|X=1]=1-a Y=1 X-1 a/2 a/2 P[Y=2|X=2]=1-B B/2 Y=2 X=2 0. BIZ y/2 X=3 V/2 Y=3 P[Y=3|X=3] = 1-y

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As a 3 was sent 3 times as much as a 1 and a 2 was sent twice as much let P1 x Th... View the full answer