In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 0.01, 0.04, 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 of the three transmitted, respectively.

Determine the following:

(a) Probability that two bits have high distortion and one has moderate distortion

(b) Probability that all three bits have low distortion

(c) Probability distribution, mean, and variance of X

(d) Conditional probability distribution, conditional mean, and conditional variance of X given that Y = 2