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Math Help - Finding mean and variance of RV

  1. #1
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    Finding mean and variance of RV

    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
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  2. #2
    Moo
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    Hello,

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