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Math Help - Joint Probability Density Function

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    Joint Probability Density Function

    The joint probability density function of a random vector (X,Y) is

    f(x,y) = 2 for 0<x<1, 0<y<1, 0<x+y<1,
    0 otherwise.

    Calculate Pr(X>Y).

    Find the conditonal density function of X given Y=0.3
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  2. #2
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    Quote Originally Posted by maibs89 View Post
    The joint probability density function of a random vector (X,Y) is

    f(x,y) = 2 for 0<x<1, 0<y<1, 0<x+y<1,
    0 otherwise.

    Calculate Pr(X>Y).

    Find the conditonal density function of X given Y=0.3
    1. Integrate the joint pdf over the region bounded by the lines y = x, x + y = 1 and y = 0.

    2. Definition: f(x | y) = \frac{f(x, y)}{g(y)} where g(y) is the marginal pdf of Y.
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