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Math Help - probability: conditioning and densities

  1. #1
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    probability: conditioning and densities

    Suppose X, Y are random variables with joint density

    f(x,y) = A^(3)xe^(-Ay) for 0<x<y
    = 0 otherwise

    a) What is the density of Y? What is E(Y)?
    b) What is E(X|Y=1)?

    --
    thanks in advance for your help!
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  2. #2
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    Quote Originally Posted by hanahou View Post
    Suppose X, Y are random variables with joint density

    f(x,y) = A^(3)xe^(-Ay) for 0<x<y
    = 0 otherwise

    a) What is the density of Y? What is E(Y)?
    b) What is E(X|Y=1)?

    --
    thanks in advance for your help!
    Marginal density: f(y) = \int_0^y A^3xe^{-Ay}dx
    Expectation of Y: E[Y] = \int_0^{\propto} y*f(y)dy

    For the second part, you need to find f(x|y=1).
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