Question:

Suppose X,Y and Z are three different random 1variables. Let X obey a Bernoulli Distribution. The probabilityr distribution function is 0.5 $=c 10(37): 0.5 a; = c. c is a constant here. Let Y obey the Standard Normal (Gaussian) Distribution, which can be written as Y M NH}, 1). X and Y are independent. Meanwhile, let Z = X Y. (a) Show that Z also follows a Normal (Gaussian) distribution. Calculate the Expectation and Variance of Z. [ths]