In the transmission of digital information, the probability that a bit has high, moderate or low distortion is 0.09,0.01,0.9 respectively. Suppose that 12 bits are transmitted and that the amount of distortion of each bit is independent.Let X and Y denote the number of bits with high and moderate distortion out of 12 bits.
a) What is the probability that one bit has high distortion and 5 bits have moderate distortion?
b) Determine the probability distribution mean and variance of X.
c) Determine the conditional probability distribution, conditional mean and conditional variance of X given that Y=11