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Quoting my text book:

Two random variables $X_{1},X_{2}$ are called independent, if:

$P(X_{1}\in A_{1}, X_{2}\in A_{2}) = P(X_{1}\in A_{1})\cdot P(X_{2}\in A_{2})$

for all $A_{1},A_{2}$ where $A_{i}$ is a subset of $\mathbb{R}$.

The 'if' in the above text confuses me.

If you have two independent variables and want to find $P(X_{1}\in A_{1}, X_{2}\in A)$ can you then just find the product of $P(X_{1}\in A_{1})$ and $P(X_{2}\in A_{2})$?

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    @Robert: Thanks for this information. But let us wait the reaction of the OP, *there is still hope*...2012-01-23

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