In transmission of digital information probability that a bit has high, moderate, or low distortion is 0.01, 0.04, and 0.95, respectively. Assume that three bits are transmitted and that amount of distortion of each bit is supposed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of three transmitted, respectively. Find out the following:
a) The probability that two bits have high distortion as well as one has moderate distortion.
b) The probability that all three bits have low distortion
c) The probability distribution, mean, and variance of X.