Linear function of random variable question - need help!?

Let Z be a standard normal random variable and let Y1 = Z and Y2 = Z^2





a) What are E(Y1) and E(Y2)?


b) What is E(Y1Y2)?


c) What is Cov(Y1,Y2)?


d) Notice that P(Y2 %26gt; 1 | Y1 %26gt; 1). Are Y1 and Y2 independent?

Linear function of random variable question - need help!?
Squaring is hardly a linear operation.





If by "standard normal random variable" you mean Gaussian distribution with mean 0 and standard deviation 1, you should make this clear.


http://en.wikipedia.org/wiki/Normal_dist...





As for Y1 and Y2, I assume you are referring to a series of random values. Are they just both drawn from Z or is Y2[i] = (Y1[i])^2? (The last question suggests the latter, but the definition suggests the former)