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Math Help - cov in transformations?

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    Question cov in transformations?

    a r.v. X is uniformily distributed between [-2,2], and Y=X2

    What is the cov(X,Y)?
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  2. #2
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    Quote Originally Posted by lauren2988 View Post
    a r.v. X is uniformily distributed between [-2,2], and Y=X2

    What is the cov(X,Y)?
    Note that for X ~ U(-2, 2) the pdf of X is f(x) = \frac{1}{4} for -2 \leq x \leq 2 and zero elsewhere.

    Cov(X, Y) = E(XY) - E(X) E(Y) = E(X^3) - E(X) E(X^2).

    Definition: E(X^n) = \int_{-\infty} ^{+\infty} x^n f(x) \, dx.

    The calculus is left for you to do.
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