Finding mean and variance of RV

**ilian** · April 18th 2010, 06:07 PM

Hello everyone,

The question asks to find the mean and variance of X = (1-Z)^(-1/2) where Z is randomly selected from [0,1].
Also recommends using a formula ${E}(x) = \int_{0} ^ \infty (1- Fx(t)) \,{d}t$
I found the pdf $fx(x) = 2/x^3$ for x= [1,infinity) and cdf $F(x)= 1-1/x^2$
Calculating ${E}(X) = \int_{-\infty}^\infty x f(x)\, {d}x$ from here gives me an answer of 2. While the previous formula that uses CDF gives a different answer. Also I'm not sure how to find the second moment E(x^2), because it does not converge.

Any input on what I could be doing wrong is appreciated.

Thank you

**Moo** · April 22nd 2010, 12:22 AM

Hello,

I think your mistake is when you say that X>1. It should be X>0.

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