Let a random variable X1 be distributed as N(0,1). Now suppose that a second random variab
Let a random variable X1 be distributed as N(0,1). Now suppose that a second random variable, X2, is constructed as the product of X1 and an independent random variable Z, which equals 1 with probability 1/2 and -1 with probability 1/2. (1)What is the (marginal) distribution of X2? (2)What is the covariance between X1 and X2? (3)What is the distribution of X1 conditional on X2?