Expected Value

**Twig** · November 18th 2009, 02:00 PM

Hi!

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

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

Are $X$ and $Y$ independant?

Thanks

**mr fantastic** · November 18th 2009, 02:10 PM

Originally Posted by Twig

Hi!

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

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

Are $X$ and $Y$ independant?

Thanks

Use this table: Dice table

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

**Twig** · November 18th 2009, 02:28 PM

Thank you

**Focus** · November 18th 2009, 05:56 PM

Originally Posted by Twig

Are $X$ and $Y$ 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?

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