- #1
Ryuuzakie
- 3
- 0
Homework Statement
[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)
Homework Equations
N/A
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 :)!