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 ?

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- Mar 20th 2010, 09:05 AMalexandrabel90expectations
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 PMmr fantastic
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 $\displaystyle x \geq 0$, $\displaystyle y \geq 0$ and $\displaystyle x + y \leq 1$. 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 PMalexandrabel90
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 AMmr fantastic
- Mar 21st 2010, 03:31 AMalexandrabel90
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 AMalexandrabel90
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 AMalexandrabel90
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 AMmr fantastic