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    The joint pdf of X and Y is given by

    f(x,y) = c(1-x-y) 0<y<1-x , 0<x<1 the < should all be less then or equal to

    (a) find the normalising constant c
    (b) find the conditional p.d.f of X given Y
    (c) are X and Y independent
    (d) E[X], and Var[X]
    (e) E[X|Y]

    For part (a) I know you have to integrate but whether it has to be a double integration, and what do you integrate with respect to first, x or y?

    If anyone can help me with any of these or guide me it would be appreciated!

    a while since I did any statistics but I seem to remember the definitions are fairly intuitive, for part (a), you have to integrate wrt y first since the max. of y depends on x, so
     \int_0^1\int_0^{1/x} f(x,y) \  dy \ dx =1
    for conditional probablilities think of the graph of f(x,y) as a surface and p(Y|X=a) as a slice though that surface at X=a. This gives some basic results, so might help:
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Updated: November 11, 2008

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