4. (Total-18%) Consider a binary symmetric channel with input X, output Y, and
transition probability a. More specifically, as shown in the figure below, the input
and output of the channel may be "0" or "1", P(Y=0|X=0)=
P(Y = 1|X = 1) = 1 - a and P(Y = 1|X = 0) = P(Y=0|X=0) = a. The
prior probability is P(X = 0) = p.
(a) (4%) Find the entropy H(Y) and the conditional entropy H(Y|X).