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    random variables

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    Prove the following:

    a) Fxy(a,b) is non-decreasing (in a and b).
    b) lim a->inf Fxy(a,b) = Fy(b)
    c) Jointly continuous random variables X and Y are independent if and only if
    fxy(x,y) = fx(x)*fy(y)

    fxy(x,y) is the joint probability density function.
    Fxy(a,b) is the joint cumulative distribution function where x y (this is not x*y) are random variables.

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    Solution Summary

    Probability of random variables is articulated.