Independence of random variables X and X^2

**student4000** · December 8th 2011, 06:48 PM

If we have two r.v.: X = { -1, 0, 1 } and Y= $X^2$ , with X uniformly distributed with probability 1/3, then X and Y are independent, right?

Pdf values of Y are 2/3 if Y=1 and 1/3 if Y=0.
I can construct joint pdf with f(x, y), such that f(i, -1) = 0, f(i, 0) = 1/9 and f(i, 1) = 2/9. Then for every f(i, j), f(x, j) = f(x)f(y), and that is the definition of independence.

Am I missing something?

**chisigma** · December 9th 2011, 01:29 AM

Saying $Y=X^{2}$ and 'X and Y are independent' is 'a little contradiction'... isn't it?...

Kind regards

$\chi$ $\sigma$

**student4000** · December 9th 2011, 03:22 AM

Yes, I have just understood that X's and Y's cannot be chosen independently.

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