Problem: A Bernoulli( 2/1 ) distributed signal X is transmitted over an additive noise channel with the ternary valued noise W:
where 0 < q < 1.
The output of the channel Y is the sum of the random variables X and W. The noise in the channel and the signal are independent.
Find:
(1) The probability density function (pdf) of Y.
(2) The cumulative distribution function (cdf) of Y.
(3) P[Y ≤ ]1 and ] P[Y > 10.
(4) The expected value of Y , that is, ] E[Y.