Problem 12E

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:

Answer

Step 1 of 4

(a)

Let denote the number of bits with high and moderate distortion of three transmitted, respectively.

We are asked to find the probability that two bits have high distortion and one has moderate distortion.

We have given

A number of possible combinations in which two bits have the high distortions can be selected is from the three bits.

Hence we can write,

Where

Hence the probability that two bits have high distortion and one have moderate distortion is