Let X and Y be independent n(0,1) random variables, and define a new random variable Z by

Question:

(a) Show that Z has a normal distribution.
(b) Show that the joint distribution of Z and Y is not bivariate normal. (Show that Z and Y always have the same sign.)

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...