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...