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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

    mathman

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    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

    HallsofIvy

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    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

    mathman

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    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?
     
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