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Math Help - joint pdf

  1. #1
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    joint pdf

    Hi, i have been given such pdf

    f(x,y) = k/y, 0<x<y, 0<y<1
    f(x,y) = 0 elsewhere

    How should i construct in order to find k?
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  2. #2
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    Quote Originally Posted by kaupehkaubu View Post
    Hi, i have been given such pdf

    f(x,y) = k/y, 0<x<y, 0<y<1
    f(x,y) = 0 elsewhere

    How should i construct in order to find k?
    Quote Originally Posted by CaptainBlack View Post
    For this problem your best policy is to draw a diagram (makes a mystic symbol in the air to ward of the wrath of Bourbaki).

    [snip]
    Have you applied this advice here? If so, it should be clear that you require the value of k such that \int_{x=0}^{x=1} \int_{y=x}^{y=1} \frac{k}{y} \, dy \, dx = 1.

    But if you reverse the order of integration the calculation is much simpler ....
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  3. #3
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    So if I reverse the order, am I going to get this?

    <br />
\int_{y=0}^{y=1} \int_{x=0}^{x=y} \frac{k}{y} \, dx \, dy = 1<br />
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  4. #4
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    Quote Originally Posted by kaupehkaubu View Post
    So if I reverse the order, am I going to get this?

    <br />
\int_{y=0}^{y=1} \int_{x=0}^{x=y} \frac{k}{y} \, dx \, dy = 1<br />
    Yes.
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