1. ## expectation and variance

say if X is the random variable, then
then the expectation E[X] is the integration of x * pdf
and the variance is the integration of x^2 * pdf - E[X]^2

what if X^2 is the random variable?
what is the expectation and variance?
is Var [X^2] = integration of x^4 * pdf - E[X^2]^2?

2. i cant quite tell what you are trying to write.

if $E(x) = \int x f(x) dx$
then
$E(g(x)) = \int g(x) f(x) dx$

so
$E(x^2) = \int x^2 f(x) dx$
$E(x^4) = \int x^4 f(x) dx$

Finally,
$Var(x^2) = E((x^2)^2) - (E(x^2))^2$
$= E(x^4) - (E(x^2))^2$

3. haha sorry! that's what I meant!
anyways, thanks for the clarification!