# Help with linear independent and correlation

1. Aug 3, 2009

### ychu066

1 Let X be a normal variable with mean 0 and variance 1. Let Y = ZX
where Z and X are independent and Pr(Z = +1) = Pr(Z = -1) =1/2.

a Show that Y and Z are independent.
b Show that Y is also normal with mean 0 and variance 1.
c Show that X and Y are uncorrelated but dependent.
d Can you write down the joint density of X and Y ? Explain your