# Expected Value

• Nov 18th 2009, 02:00 PM
Twig
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
• Nov 18th 2009, 02:10 PM
mr fantastic
Quote:

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.
• Nov 18th 2009, 02:28 PM
Twig
Thank you
• Nov 18th 2009, 05:56 PM
Focus
Quote:

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?