3. Let X be a standard normal random variable and Z is an independent random variable satisfying P[Z = 1] = P[Z = -1] = NIK In class we define Y = XZ and showed that Y is standard normal. We establish that although X and Y are uncorrelated, they are not indepen dent. In this excercise, we use moment-generating functions to show that Y is standard normal and X and Y are not independent. a. Establish the joint moment-generating function formula 2 b. Use the formula above to show that Efe" ] = e?". This is the moment-generating function for a standard normal random variable, and thus Y must be a standard normal random variable. c. Show that X and Y are NOT independent