- #1

- 13

- 0

## Main Question or Discussion Point

How do I prove that the mean of a random variable Z which is the sum of to other random variables X and Y is the sum of the mean of X with the mean of Y?

- Thread starter Mppl
- Start date

- #1

- 13

- 0

How do I prove that the mean of a random variable Z which is the sum of to other random variables X and Y is the sum of the mean of X with the mean of Y?

- #2

mathman

Science Advisor

- 7,767

- 417

- #3

- 13

- 0

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

thank you.

- #4

- 525

- 5

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).

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

thank you.

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

- 7,767

- 417

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.

- Last Post

- Replies
- 2

- Views
- 5K

- Replies
- 15

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 8

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 4K

- Replies
- 15

- Views
- 4K

- Last Post

- Replies
- 2

- Views
- 3K

- Replies
- 10

- Views
- 3K

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 11

- Views
- 2K