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Thread: Conditional distribution

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    Conditional distribution




    Let X be a random variable.
    Given:
    -P(X = 1) = 1/2
    -P(X = 2) = 1/2
    -The conditional distribution of Y given X is an exponential with rate X.

    Find the expectation and variance of Y


    I can't wrap my head around conditional distribution. Anyone care to help?

  2. #2
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    Re: Conditional distribution


    I think you can simplify the problem by noting that

    f(y) = e^{-y} with probability 1/2, and

    f(y) = 2e^{-2y} with probability 1/2.

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