(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] f\left(x,y\right)=\left\{\begin{array}{cc}\frac{1}{y} ,&\mbox{ if }

0 \leq x \leq y, 0 \leq y \leq 1 \\ 0,&mbox{ otherwise } \end{array}\right. [/tex]

Find the marginal distributions (pdf and cdf) of X and Y

Find Pr(X+Y>0.5)

2. Relevant equations

N/A

3. The attempt at a solution

Finding the marginal distribution of X, I get,

[tex]f_X(x) = \int_{0}^{1} \frac{1}{y} dx [/tex]

[tex]f_X(x) = ln \left(y\right)\right|_0^1 [/tex]

But ln (0) does not exist, and ln (1) = 0... so I'm thinking I'm doing this wrong.

Also, with the second part of the problem, I get:

[tex]Pr(X+Y \geq 0.5)=1- \left[0.5 ln \left(y\right) - y\right]_0^1[/tex]

And as before, I'm stuck with an ln(0).. any assistance would be appreciated :)!

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# Homework Help: Joint Probability functions (finding marginals)

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