Let x1nbspand x2nbsphave a bivariate gaussian pdf with

Question

Let X₁ and X₂ have a bivariate Gaussian PDF with correlation coefficient ρ₁₂ such that each X_i is a Gaussian (µ_i, σ_i) random variable. Show that Y = X₁X₂ has variance 

You may also need to look ahead to Problem 6.3.4.

Problem 6.3.4

Let X be a Gaussian (0,σ) random variable. Use the moment generating function to show that

Let Y be a Gaussian (µ, σ ) random variable. Use the moments of X to show that