
E(x^2) and V(x^2)
Explosive devices used in mining operations produce nearly circular craters when detonated. The radii of these craters are exponentially distributed with mean 10 feet. Find the mean and variance of the areas produced by these explosive devices.
I tried to derive
E(pi X^2) and Var ( pi X^2) where E(X)=10 using the formula
E(X) = integrate (X. i/r. exp (x/r) ) from neg infinity to infinity but i couldnt get the answer...
thanks!

You should be able to integrate these, but that's not the point of these problems.
AND an exponentially distributed rv is nonzero on ZERO to infinity.

then how should i go about solving this question?
thanks!

$\displaystyle E(aX^2)=aE(X^2)$
and $\displaystyle E(X^2)=V(X)+(E(X))^2$
you should know the mean and variance of an exponential or you can look it up.
If you can't do that, you can always integrate.

to find the var(L) , it will be var(L) = 900 Var(Y) + 4 Var(Y^2)
how do i find the var (Y^2)?
