In the transmission of digital information, the probability that a bit has high, moderate and low distortion is 0.01, 0.04 and 0.95 respectively. Suppose that three bits of information are transmitted and the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three respectively. Determine:
(a) fxy(x,y)
(b) fx(x)
(c) E(X)
(d) fY|1(y)
(e) E(Y|X = 1)
(f) Are X and Y independent?
