Consider a binary input Q-ary output discrete memory less channel. The channel is said to be symmetric

Question:

Consider a binary input Q-ary output discrete memory less channel. The channel is said to be symmetric if rite channel transition probability p(j|i) satisfies the condition: p(j|0) = p(Q– 1 –j|1), j = 0,1,...,Q – 1 suppose that the channel input symbols 0 and 1 are equally likely. Show that the channel output symbols are also equally likely; that is, P(j) = 1/Q, j = 0,1 , . . ., Q – 1