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Math Help - Multivariate Probability Distributions

  1. #1
    Junior Member atalay's Avatar
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    Multivariate Probability Distributions

    If the random variables X and Y have the joint pdf:

    f (x, y)= { cx^2y for x^2<=y<=1
    0, elsewhere

    Find c?
    i know

    \int_a^b \int_c^d f(x, y) dxdy=1 for a<y<b, c<x<d.

    Therefore, for finding c,

    \int_1^0 \int_x2^1
    is it rigt?
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by atalay View Post
    If the random variables X and Y have the joint pdf:

    f (x, y)= { cx^2y for x^2<=y<=1
    0, elsewhere

    Find c?
    i know

    \int_a^b \int_c^d f(x, y) dxdy=1 for a<y<b, c<x<d.

    Therefore, for finding c,

    \int_1^0 \int_x2^1
    is it rigt?
    Draw the region defining the support. Then it is crystal clear that you require \int_{x = -1}^{x = 1} \int_{y = x^2}^{y = 1} f(x, y) \, dy \, dx = 1.
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