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A faster method to check whetherXand Yare independent:

If we find that the joint p.d.f. or joint p.m.f. of X and Y can be written as:

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&o o see that the fnctiong(x)actall depends onyand therefore 0* satisfing the

condition re6ired for + and to be independent!

An example for correlation:

To illustrate how the correlation measures the intensity of the concentration of

the probability for Xand Yabout a line, let these random variables have a

distribution that is uniform over the area in the following gure:

That is the joint p.d.f. of and ! is:

e!sewhere

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