3
$\begingroup$

I have a fundamental question regarding conditional probability. Lets say I have $n$ independent random variables $X_1, X_2, \ldots, X_n$. Another random variable, $W$ is conditioned on the conjunction of these random variables: $P(W | X_1, X_2, X_3, \ldots, X_n)$. Given that $X_1, \ldots, X_n$ are independent, is it possible to write

$$P(W | X_1, X_2, X_3, \ldots, X_n) = P(W | X_1) \cdot P(W | X_2) \cdot \cdots \cdot P(W | X_n).$$

Or is the only way to rewrite is the Bayes theorem?

  • 0
    You can use $\TeX$ on this site by enclosing formulas in dollar signs; single dollar signs for inline formulas and double dollar signs for displayed equations. You can see the source code for any math formatting you see on this site by right-clicking on it and selecting "Show Math As:TeX Commands". [Here](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference)'s a basic tutorial and quick reference. There's an "edit" link under the question.2012-09-27

2 Answers 2