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Math Help - joint distribution problem

  1. #1
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    joint distribution problem

    The density fnc. of X and Y is
    f(x,y)=x+y for 0<x<1, 0<y<1 and 0 otherwise.

    a-Are X and Y independent?
    b-Find the density function of X
    c- Find P(X+Y<1)
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  2. #2
    MHF Contributor matheagle's Avatar
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    (a) dependent by inspection, the joint density does NOT factor.

    (b) f_X(x)=\int_0^1 f(x,y)dy=x+.5 on (0,1).

    and I'll let you do

    (c) \int_0^1\int_0^{1-x} f(x,y)dydx.
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