Answered: Given the joint density for -y

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Given the joint density for -y

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.2: Perimeter And Area Of Polygons

Problem 47E

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Question

Given the joint density
for -y <x<y and 0 < y<1
f(x, y) :
elsewhere
show that the random variables X and Y are uncorrelated but not independent.

Expert Solution

Step 1

The joint density function is given below:

|1 -y<x<y and 0< y <1
f (x.y) =
elsewhere

Step 2

The marginal density function of X is as follows:

The marginal density function of Y is as follows:

-jл
f(x)- [s(х)dy
J-0
| lcy
[ldy
= 1,
—у «х<у
f (v) = [ f(x.y)dx
X--y
| lax
0<y <1
= 2y,

Step 3

If the random variables X and Y are uncorrelated, we have to show that their covariance has to be Zero.

Step by step

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