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Math Help - Normal distribution problems.

  1. #1
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    Normal distribution problems.

    Let X~N(μ,σ^2).

    Determine
    (a) Compute E[(X-μ)^4)]
    (b) Compute E[|X-μ|]
    (c) Define Y = (X-μ)^2. Determine the distribution of Y, and find the expected value of 1/Y.


    At the first time, I thought that E[(X-μ)^4)] is same with Var(X^2). Is it true?
    And how can I solve the other problems?
    Last edited by perh; November 18th 2013 at 03:35 AM.
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  2. #2
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    Re: Normal distribution problems.

    Hey perh.

    Hint: For these problems, use the definition of expectation (and variance) in integral form. For c) I'd suggest looking at the MGF of the expectation of the transformed variable and compare it to a known table of MGF's.
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