Suppose X is binary valued random variable with probabilities P(X = 1) = 0.2, P(X = 2) = 0.8 Suppose we record noisy measurements Yk of X at times k = 1, 2, . . . where P(Yk = 1|X = 1) = 0.8, P(Yk =...

Suppose X is binary valued random variable with probabilities P(X = 1) = 0.2, P(X = 2) = 0.8 Suppose we record noisy measurements Yk of X at times k = 1, 2, . . . where P(Yk = 1|X = 1) = 0.8, P(Yk = 2|X = 2) = 0.6 Given Y1 = 2. Compute P(X = 1|Y1), and compute E{X|Y1}. Given Y1 = 2, Y2 = 2. Compute P(X = 1|Y1, Y2), and compute E{X|Y1, Y2}.