Expected value of bivariate pdf

  • Thread starter boneill3
  • Start date
  • #1
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Main Question or Discussion Point

Is the expected value E[x]or E[y] of a bivariate pdf fXY(xy)

\int x f(x,y)dx

or

E[y]

\int y f(x,y)dy ?

example if f(x,y) = x+y

E[X] = \int x *(x+y)dx


regards
Brendan
 

Answers and Replies

  • #2
mathman
Science Advisor
7,757
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You need to carry out the double integral. A single integration gives the conditional expection of one variable with rexpect to the other.
 
  • #3
127
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So just say you had the lmits of 0<x<1 0<y<1
The expected value would be:
[itex]
E[X] = \int_{0}^{1}\int_{0}^{1} x *(x+y)dxdy

= 7/12
[\latex]
Is that right?
 
  • #4
127
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Sorry,

[itex]
E[X] = \int_{0}^{1}\int_{0}^{1} x *(x+y)dxdy

= 7/12
[/itex]

regards
 

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