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    Random Variables

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    Suppose X1 and X2 are independent exponential (λ) random variables. Let Y1=X1-X2 and Y2=X2.

    a) Find the joint density of Y1 and Y2.
    b) Find the marginal density of Y1.

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    https://brainmass.com/statistics/probability/random-independent-exponential-variables-11951

    Solution Preview

    because,
    p(X1,X2) = p(X1)*p(X2) = l^2*exp(-l(X1+X2))
    raed l as lembda.
    del(Y1)/del(X1) = 1
    del(Y1)/del(X2) = -1
    del(Y2)/del(X1) = 0
    del(Y2)/del(X2) = ...

    Solution Summary

    Suppose X1 and X2 are independent exponential (λ) random variables. Let Y1=X1-X2 and Y2=X2.

    a) Find the joint density of Y1 and Y2.
    b) Find the marginal density of Y1.

    $2.19

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