Ternary Channel. A communication system transmits three signals, s1, s2, or s3, with equal probabilities. The reception is corrupted by noise, causing the transmission to be changed according to the...

Ternary Channel. A communication system transmits three signals, s1, s2, or s3, with equal probabilities. The reception is corrupted by noise, causing the transmission to be changed according to the following table of conditional probabilities:

The entries in this table list the probability that sj is received, given that si is sent, for i, j = 1,2,3. For example, if s1 is sent, the conditional probability of receiving s₃
is 0.15.

(a) Compute the probabilities that s₁, s₂, and s₃
are received.

(b) Compute the probabilities
  (Complete the table.)