Expected value of bivariate pdf

[boneill3]

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

 

[mathman]

You need to carry out the double integral. A single integration gives the conditional expection of one variable with rexpect to the other.

 

[boneill3]

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?

 

[boneill3]

Sorry,

$E[X] = \int_{0}^{1}\int_{0}^{1} x *(x+y)dxdy = 7/12$

regards