1. A communication channel consists of two inputs (X1, X 2) and three outputs (Y1, Y2, Y3). Each input-output path is described by a transition probability pi}, standing for P1\"(Y}- = y,|X, = xi), j = 1, 2, 3 and i = 1,2. Thus, 13,,- is the conditional probability of receiving output )2; given that the input is xi. This set of transition probabilities can be determined by conducting transmission experiments. Accordingly, the channel transition is summarized by J' I. [0.92 0.05 0.03 0.02 0.88 0.10 The input probabilities are Pr(X1) = 0.4 and Pr(X2) = 0.6. a) Find the output probabilities Frog), j = 1, 2, 3. b) Determine Pr(X,- = x,|1f,- = yj), t: = 1,2, j = 1,2,3. 0) Compute the probability of error P8 = Pr(x1, not 371) + Pr(x2, not 312). Comment on the complexity of calculation in parts (a), (b) and (0) when i and j are large. Suggest a systematic approach to handle the computation