(ii) Two BSC's are connected in cascade as shown in the figure. 0.8 Y1 0.7 X, 2 0.2 X 0.3 0.2 0.3 Z 0.8 Y2 0.7 (a)Find the Channel Matrix of the resultant channel. (b)Find P (21) and P (22), if P(X) -0.6, P(X) =0.4 7. (1)Prove that the Mutual information of the channel is Symmetric. I(X,Y)=1(Y, X) (6 marks) (ii)Prove that the mutual information is always positive I(X, Y) 20 (6marks) 8. Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y