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Math Help - Valid joint probability density function?

  1. #1
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    Valid joint probability density function?

    I have to show that this is a valid joint probability density function. My understanding is that this is valid when the integral is equal to 1. My question is, how to do I do a joint integration when only one of the variables is in play?

    f(x,y) = 1/y for 0<x<y, 0<y<1

    I appreciate the help!
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  2. #2
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    Re: Valid joint probability density function?

    Quote Originally Posted by drabbie View Post
    I have to show that this is a valid joint probability density function. My understanding is that this is valid when the integral is equal to 1. My question is, how to do I do a joint integration when only one of the variables is in play?
    f(x,y) = 1/y for 0<x<y, 0<y<1
    Is the function non-negative everywhere?

    What is \int_0^1 {\int_0^y {\frac{1}{y}dxdy} }=~?
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  3. #3
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    Re: Valid joint probability density function?

    They did not specifically say 0 elsewhere, but I assume it is non-negative outside of the limits. I will try it like that, thank you.
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