2 Information Theory Suppose the joint probability distribution of two binary random variables X and Y are given as follows. 1 X\Y 0 1 0 1 0 (a) Find entropy H(X) and H(Y). (b) Find conditional entropy H(XY) and H(Y|X). (c) Find mutual information I(X; Y). (d) Find joint entropy H(X, Y). (e) Suppose X and Y are independent. Show that H(YX) = H(Y) (f) Suppose X and Y are independent. Show that H(X,Y) = H(X) + H(Y) (g) Show that I(X; X) = H(X) For all the above, show your work, step by step. No points will be given otherwise.