- Basic Idea: Compute the expectation or variance of a (complicated) random variable by conditioning on another random variable.
- In stochastic process, it is often useful to condition on the first event
- Use of the formula
![E[X] = E[E[X|Y]]](http://mytechroad.com/wp-content/ql-cache/quicklatex.com-47def80fc1e063a369b2496d4a69ee15_l3.png "Rendered by QuickLaTeX.com")
![var[X] = var[E[X|Y]] + E[var[X|Y]]](http://mytechroad.com/wp-content/ql-cache/quicklatex.com-56bdb0381b9c29705e864947b01b7e1e_l3.png "Rendered by QuickLaTeX.com")
Example:
Computing Expectation by Conditioning