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Math Help - Moment-Generating and Expected Value

  1. #1
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    Moment-Generating and Expected Value

    a) Suppose the height of a rectangle is twice its width and the width is a uniform distribution over [0,6]. Find the expected area of the rectangle.
    b) Let X have m.g.f. of Mx(t) = (1-5t)^-2 for t<1/5. Find the Var(X)
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  2. #2
    MHF Contributor matheagle's Avatar
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    a) A=HW=2W^2

    SO E(A)=2E(W^2)={1\over 3}\int_0^6 w^2dw

    b) you can differentiate twice and let t=0 to get the first two moments
    From that you can get the variance.
    However this is a gamma and you can obtain the variance by inspection.
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