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Math Help - Gumbelís bivariate exponential distribution

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    Gumbelís bivariate exponential distribution

    Suppose that (X, Y ) can be described by the joint CDF:

    FX,Y (x, y) = 1 - e^{-x} - e^{-y}+ e^{-(x+y+(theta)xy)}

    Show That

    FX,Y (x, y) = e^{-x-y-(theta)xy}[(1 + \thetax)(1 + \thetay) − \theta] , x, y > 0, \theta [0, 1].

    Suppose that \theta = 0. Explain why X and Y are independent?

    Show that fX(x) = e−x, x > 0. (use \lambda = 1 + \thetax

    Calculate fY|X(y|x) and use it to compute E[Y|X = x]

    N.B (where i have used the word "theta", obviously i have meant to use the symbol, but i was having problems doing latex math inside of latex math so used the word, so on each occasion where it is used, it should read " \thetaxy" hope it doesnt cause confusion)
    Last edited by sirellwood; November 12th 2009 at 11:22 AM.
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