- #1

- 13

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Mppl
- Start date

- #1

- 13

- 0

- #2

mathman

Science Advisor

- 7,924

- 467

- #3

- 13

- 0

I'm trying to prove it and I'm getting a convultion integral so far...

thank you.

- #4

- 530

- 7

I'm trying to prove it and I'm getting a convultion integral so far...

thank you.

Yes that'll eventually give you a proof for the special case where the rv's are independent and have densities (involves reversing the order of integration and a change of variables).

Another approach that would work for the non-independent case is to consider separately the joint distribution and marginal distributions of X and Y.

- #5

- 13

- 0

- #6

mathman

Science Advisor

- 7,924

- 467

E(X+Y)=∫∫(x+y)dF(x,y)=∫∫xdF(x,y) + ∫∫ydF(x,y).

Integrate with respect to y in the first integral and integrate with respect to x in the second integral. You will be left with E(X) + E(Y).

In the above F(x,y) is the joint distribution function.

Share:

- Replies
- 4

- Views
- 3K