In man},r comnnmication channels3 the output signal can often times be calculated as a linear transformation of the input signal. To design mmm1mication algorithms for such channeLs, it is important to understand the relationship between the different properties of the input and output signals based on the channel parameters. In this problem, consider that the input to the channel is a continuous random 1variable X. The output of the channel is a random variable Y dened as Y = aX + b. HereJ a and b are channel parameters and a :5 0. Let (IF); (1:!) he the characteristic fllti of X. (a) Let 'I'y (in) be the characteristic function of Y. Determine Iiiy{w) in terms of in; (w), a, and b. Show the process for determining this relationship. (b) Assume that X ~ Exp()) and that b = 0. Using the characteristic function of Y, determine what kind of random variable Y is. (c) Again, assume that X ~ Exp(A). First, use the properties of expectation to find EY]. Now, use the characteristic function of Y to find ELY . Answers are in terms of a, b, and 1