Category:Definitions/Conditional Expectation
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This category contains definitions related to Conditional Expectation.
Related results can be found in Category:Conditional Expectation.
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.
Pages in category "Definitions/Conditional Expectation"
The following 9 pages are in this category, out of 9 total.
C
- Definition:Conditional Expectation
- Definition:Conditional Expectation on Sigma-Algebra
- Definition:Conditional Expectation/Also known as
- Definition:Conditional Expectation/Discrete Case
- Definition:Conditional Expectation/General Case
- Definition:Conditional Expectation/General Case/Event
- Definition:Conditional Expectation/General Case/Random Variable
- Definition:Conditional Expectation/General Case/Sigma-Algebra
- Definition:Conditional Mean