In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.10, and 0.95, respectively. Suppose that three bits are transmitted and that 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?