1 Let X be a normal variable with mean 0 and variance 1. Let Y = ZX(adsbygoogle = window.adsbygoogle || []).push({});

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

answer.

Note that this example exhibits two random variables which are un-

correlated, normally distributed, but not independent (and necessarily

not jointly normally distributed).

Please help me with the bold questions.....

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# Help with linear independent and correlation

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