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Homework Help: Joint Probability functions (finding marginals)

  1. May 3, 2010 #1
    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 :)!
     
  2. jcsd
  3. May 3, 2010 #2

    lanedance

    User Avatar
    Homework Helper

    note that [itex] f_{X,Y}(x,y) [\itex] is only non-zero for the triangle given by x = 0, y= 1 & y=x

    so you may need to rethink your integration limits...
     
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