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Homework Help: Marginal Density Fx (x)

  1. Aug 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Calculate the marginal density of fx (x).
    Fx,y (x,y) = double integral of 4x.e^(x+y) when 0<x<y, 0 otherwise.


    2. Relevant equations



    3. The attempt at a solution

    i set up the equation as fx (x) = integral from x up to infinity of 4x.e^(x+y) dy

    i get 4x [e^(x+y)] from x to infinity,

    thats when the problem arises as whatever i do there's always infinity in the question.

    I'm told the answer is 4x.e^(-2x)

    any help would be really appreciated.
    thanks.
     
  2. jcsd
  3. Aug 15, 2010 #2

    lanedance

    User Avatar
    Homework Helper

    are you sure you haven't missed a minus sign in the original distribution>
    [tex] f_{X,Y} (x,y)dxdy = 4xe^{-(x+y)}dx dy [/tex]

    would make more sense, the distrubution you gave is unbounded
     
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