# E(x^2) and V(x^2)

• Mar 6th 2010, 01:41 AM
alexandrabel90
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!
• Mar 6th 2010, 07:17 AM
matheagle
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.
• Mar 6th 2010, 08:06 AM
alexandrabel90
then how should i go about solving this question?

thanks!
• Mar 6th 2010, 08:24 AM
matheagle
$E(aX^2)=aE(X^2)$

and $E(X^2)=V(X)+(E(X))^2$

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.
• Mar 7th 2010, 12:34 AM
alexandrabel90
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)?
• Mar 7th 2010, 07:36 AM
matheagle