Let X1 and X2 have a bivariate Gaussian PDF with correlation coefficient ρ12 such that each Xi is a Gaussian (µi, σi) random variable. Show that Y = X1X2 has variance ![](https://test.transtutors.com/qimg/6c1c1d49-c6b4-40e5-9790-522be9daede0.png)
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
![](https://test.transtutors.com/qimg/99f50a03-1fee-4d2d-b862-57bcd1ca0053.png)
Let Y be a Gaussian (µ, σ ) random variable. Use the moments of X to show that
![](https://test.transtutors.com/qimg/5f2ded2c-9733-4096-8818-ddd589c0db12.png)