Given random variables X and Y, which are not independent, is it always possible to find a random variable W which is independent from X, such that Y = f(X,W), for some function f?(adsbygoogle = window.adsbygoogle || []).push({});

Example: let the joint distribution of X and Y be

Then if we let W have the Bernoulli distribution with p = 1/3, and f(x,w) = x XOR w, we haveCode (Text):

Y 0 1

X+-------

0|1/3 1/6

1|1/6 1/3

y = f(X,W).

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# Decomposition of a R.V. into dependent and independent parts

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