# expectations

• Mar 20th 2010, 09:05 AM
alexandrabel90
expectations
Given that (X,Y) have pdf f(x,y)=2 and x+y=1. How do i find E(X+Y).

how doi decide the range tt i should integrate from since it cant be from infinity to neg ininty ?
• Mar 20th 2010, 02:14 PM
mr fantastic
Quote:

Originally Posted by alexandrabel90
Given that (X,Y) have pdf f(x,y)=2 and x+y=1. How do i find E(X+Y).

how doi decide the range tt i should integrate from since it cant be from infinity to neg ininty ?

I doubt that you have posted the whole question exactly as it was originally stated.

eg. The question probably said that the support was the region bounded by $x \geq 0$, $y \geq 0$ and $x + y \leq 1$. In which case, you set up the appropriate double integral of f(x, y) over that region.

Have you been taught double integration at all?
• Mar 20th 2010, 02:46 PM
alexandrabel90
yes i was taught how to use double integral. iwas thinking tt i need to findE(X) andE(Y) seperatedly.in tt case, wewont need to usedouble integral right?
• Mar 21st 2010, 02:01 AM
mr fantastic
Quote:

Originally Posted by alexandrabel90
yes i was taught how to use double integral. iwas thinking tt i need to findE(X) andE(Y) seperatedly.in tt case, wewont need to usedouble integral right?

You would then need the marginals.

Calculate $\int \int_{R_{xy}} (x + y) f(x, y) \, dx \, dy$ where $R_{xy}$ is region of integration.

(And you still have not said whether you posted the complete question or not).
• Mar 21st 2010, 03:31 AM
alexandrabel90
sorry i missed tht part of the question. i just checked and the region that u said is the correct region that the question is asking for. sorryfor that mstake.
• Mar 21st 2010, 03:41 AM
alexandrabel90
the complete question is let (X,Y) have bivariate pdf f(x,y)=2 and bounded by x+y=1 in the first quadrant. find E(X+Y).
• Mar 21st 2010, 03:46 AM
alexandrabel90
may i know what is the region of integration?

initially what i did was integrate from 0 to (1-y) for xf(x,y)dx + integrate from 0 to (1-x) yf(x,y)dy ...i was trying to use marginals..but i wasnt sure what is the range that i should integrate from...

from my working above, the range that i have integrated is obviously wrong..

if i were to use your method, would the range be form 0 to (1-y) dx and then 0 to 1 dy?

thanks!
• Mar 22nd 2010, 02:15 AM
mr fantastic
Quote:

Originally Posted by alexandrabel90
may i know what is the region of integration?

initially what i did was integrate from 0 to (1-y) for xf(x,y)dx + integrate from 0 to (1-x) yf(x,y)dy ...i was trying to use marginals..but i wasnt sure what is the range that i should integrate from...

from my working above, the range that i have integrated is obviously wrong..

if i were to use your method, would the range be form 0 to (1-y) dx and then 0 to 1 dy?

thanks!

Yes.