My question is attached below.

Let Y be a Gaussian random variable with mean / and variance o. Define the random variable X = e . In the followings provide complete derivations and explanations of results. a) Find the PDF of X. b) Find the expectation of X. c) Find the variance of X. d) Find the n-th order moment of X. e) Find the Moment Generating Function (MGF) of X. Assume now that random variables Yo , i = 1,..., N are independent identically distribute Gaussian with mean a and variance o2. Let X; = eVi, i = 1,..., N, and consider the random variable defined as N Z = X1 . X2 .. . .' XN = Xi i=1 f) Find the PDF of Z