# How do you apply Bayes' theorem to continuous random variables?

Aug 2, 2016

The same for events

#### Explanation:

The same for events

For events
$p \left(B | A\right) = \frac{P \left(B\right) P \left(A | B\right)}{P \left(A\right)}$

For two continuous random Variables

${f}_{X} \left(x | Y = y\right) = \frac{{f}_{X} \left(x\right) {f}_{X} \left(x | Y = y\right)}{{f}_{Y} \left(y\right)}$