I have calculated var y varx Ey Ey2 But i have no idea how t

I have calculated: var (y), var(x), E(y), E(y^2)

But i have no idea how to calculate E(X,Y)

Suppose that a random variable X satisfies E(X) = E(X^3) = 0 E(X^2) = 1 E(X^4) = 3. and let Y = u -I- bX + cX^2. Express the correlation coefficient p(X. Y) as a function of a, b and C.

Solution

E(XY) = E[ax+bX^2+cx^3]

= aE(X)+bE(X^2)+cE(X^3)

= a.0+ b.1+c.0

=b