Lesson 9

Another simple but frequently used property of expectation: for \(\chi_{A}\), the indicator random variable of an event \(A \subseteq U\), it holds that \[\operatorname{E}[\chi_{A}]=\Pr[A] \ .\] Indeed, \[\operatorname{E}[\chi_{A}]=0 \cdot \Pr[\overline{A}]+1\cdot \Pr[A]=\Pr[A] \ .\]