Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Joint problem density function problem

  1. Apr 15, 2015 #1
    I need help guys I cant understand this
    Can anyone explain thoroughly how do I form the range for this question?
    f(x,y)= e-x for 0≤x≤y≤∞
    0 Otherwise

    Find P(x+y≤1)
    I attempted this by integrating through the range of
    0≤y≤(1-x) and 0≤x≤∞ but that doesn't seem right
  2. jcsd
  3. Apr 15, 2015 #2


    User Avatar
    Science Advisor
    Gold Member

    The statement is confusing. You appear to have a density function in x and y, which is a function of x only.
  4. Apr 15, 2015 #3
    Hello mathman there's a slight error with range I made in the question which is 0≤y≤x≤∞
    There was no other problems with the question as I was asked this way.
  5. Apr 16, 2015 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    No, [itex]f(x,y)= e^{-x}[/itex] for [itex]0\le x\le y\le A[/itex] is a function of both x and y. To determine "A", use the fact that the "total" probability must be 1:
    [tex]\int_{y= 0}^A\int_{x= 0}^y e^{-x} dx dy= 1[/tex]
  6. Apr 16, 2015 #5


    User Avatar
    Science Advisor
    Gold Member

    Getting an equation for A is easy enough. [itex]A+e^{-A}=2[/itex]. I am confused as to what is the question.
  7. Apr 16, 2015 #6
    Will I be able to find P(x+y≤1) after determine A?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Joint problem density function problem