Math Help - cov in transformations?

1. cov in transformations?

a r.v. X is uniformily distributed between [-2,2], and Y=X2

What is the cov(X,Y)?

2. Originally Posted by lauren2988
a r.v. X is uniformily distributed between [-2,2], and Y=X2

What is the cov(X,Y)?
Note that for X ~ U(-2, 2) the pdf of X is $f(x) = \frac{1}{4}$ for $-2 \leq x \leq 2$ and zero elsewhere.

$Cov(X, Y) = E(XY) - E(X) E(Y) = E(X^3) - E(X) E(X^2)$.

Definition: $E(X^n) = \int_{-\infty} ^{+\infty} x^n f(x) \, dx$.

The calculus is left for you to do.