1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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...
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook