- #1

Gridvvk

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- 1

## Homework Statement

The problem is in the context of a probability problem; however, my question in regards to a computation regarding a particular integral. All that is needed to know is that the probability density function is 1 in the range 0 < y < 1 , y-1 < x < 1 - y, and 0 otherwise.

I need to find E(XY) and E(|XY|).

## Homework Equations

[tex] E(XY) = \int_0^{1} \int_{y-1}^{1-y}\ XY \ dx dy[/tex]

[tex] E(|XY|) = \int_0^{1} \ \int_{y-1}^{1-y} \ |XY| \ dx dy[/tex]

## The Attempt at a Solution

E(XY) = 0. Simple calculation.

For E(|XY|) however, I am getting 1/24, but WolframAlpha computes it out to be 1/12.

I am doing:

[tex] E(|XY|) = \int_0^{1}\ \int_{y-1}^{1-y}\ |XY| \, dx dy[/tex] = [tex]

\int_0^{1} \int_0^{1-y} \ XY \, dx dy[/tex]

I am not sure why this is incorrect. Making the lower bound of x 0 worked for me when I was computing E(|X|), but is giving me half the answer for E(|XY|).

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