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Joint Probability Density Function

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data

    The joint probability density function of X and Y is given by
    f(x, y) = c( x3 + xy/4 )
    
    0 < x < 1
    0 < y < 2

    (a) For what value of c is this a joint density function?
    (b) Using this value of c, compute the density function of Y .
    (c) Using this value of c, nd PfX > Y g.

    3. The attempt at a solution

    I'm looking through my notes and i can't find anything that helps me solve A... :(
     
  2. jcsd
  3. Feb 25, 2013 #2

    LCKurtz

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    The double integral, over the region, of the density function must be 1.
     
  4. Feb 26, 2013 #3
    So the idea is, if i do a double integral on this function i should end up with c * some value, and i need to find a value for c such that c * some value = 1?
     
  5. Feb 26, 2013 #4

    Ray Vickson

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    Try it yourself to see!
     
  6. Feb 26, 2013 #5
    So i did it and i ended up with 3/4 * c... So the idea now is that i want C to equal 1?

    And how would i start computing the density function of Y?
     
    Last edited: Feb 26, 2013
  7. Feb 26, 2013 #6

    Ray Vickson

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    Do you not understand that you want the double integral = 1? That means that you need to equate your result to 1.

    As to the density of Y: it will just be the *marginal* density of Y. The meaning of this was already dealt with in another thread.
     
  8. Feb 28, 2013 #7
    Okay i've managed to figure out everything except for the last question. I have formulas for P( X ≤ x ) but it's asking me to find P( X < Y ).
     
  9. Feb 28, 2013 #8

    LCKurtz

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    Draw a picture of that region inside your given domain and integrate the joint density over it.
     
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