Symbols:E/Conditional Expectation
Jump to navigation
Jump to search
Conditional Expectation
- $\expect {X \mid B}$
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $X$ be a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.
Let $B$ be an event in $\struct {\Omega, \Sigma, \Pr}$ such that $\map \Pr B > 0$.
The conditional expectation of $X$ given $B$ is written $\expect {X \mid B}$ and defined as:
- $\expect {X \mid B} = \ds \sum_{x \mathop \in \image X} x \condprob {X = x} B$
where:
- $\condprob {X = x} B$ denotes the conditional probability that $X = x$ given $B$
whenever this sum converges absolutely.
The $\LaTeX$ code for \(\expect {X \mid B}\) is \expect {X \mid B}
.