Question
Asked Dec 15, 2019
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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.
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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.

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Expert Answer

Step 1

The joint density function is given below:

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

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Step 2

The marginal density function of X is as follows:

The marginal density function of Y is as follows:

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-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,

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Step 3

If the random variables X and Y are uncorrelated, we have to...

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Cov (x,y) =0 E(xy) - E(x) E(y) = 0

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