If two random variables X and Y are independent, are they also un-correlated ? Separately, if...

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If two random variables X and Y are independent, are they also un-correlated ? Separately, if...

If two random variables X and Y are independent, are they also un-correlated ? Separately, if X and Y are un-correlated are they also independent ? When is the second statement always true ?

math Statistics-And-Probability

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Answer 1

Answer #1

(a)

Answer:

Yes

EXPLANATION:

If two random variables are independent, then they are un-correlated.

(b)

The statement, "If X and Y are un-correlated, they are also independent" is always true only when f(X) and g(Y) are un-correlated for all functions f(.) and g(.).

EXPLANATION:

Correlation only means linear relation. Independent random variables are unrelated up to any functional transformation. Correlation is a measure of linear dependence. It is possible for two random variables X and Y to be uncorrelated but nonlinearly dependent.

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Answer 2

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If two random variables X and Y are independent, are they also un-correlated ? Separately, if...

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