1. ## Expected Value

Hi!

Problem: A die is rolled twice. Let $\displaystyle X$ denote the sum of the two numbers that turn up, and $\displaystyle Y$ the difference of the numbers (specifically, the number on the first roll minus the number on the second roll). Show that

$\displaystyle E(XY)=E(X)\cdot E(Y)$

Are $\displaystyle X$ and $\displaystyle Y$ independant?

Thanks

2. Originally Posted by Twig
Hi!

Problem: A die is rolled twice. Let $\displaystyle X$ denote the sum of the two numbers that turn up, and $\displaystyle Y$ the difference of the numbers (specifically, the number on the first roll minus the number on the second roll). Show that

$\displaystyle E(XY)=E(X)\cdot E(Y)$

Are $\displaystyle X$ and $\displaystyle Y$ independant?

Thanks
Use this table: Dice table

to get the distribution for X, Y and XY. Then calculate the required expectations.

3. Thank you

4. Originally Posted by Twig
Are $\displaystyle X$ and $\displaystyle Y$ independant?
.

What is the probability that the difference is 11? If I told you they sum up to 2, what is the probability that they have difference 11?