Category:Total Expectation Theorem
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This category contains pages concerning Total Expectation Theorem:
Let $\EE = \struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $X$ be a discrete random variable on $\EE$.
Let $\set {B_1 \mid B_2 \mid \cdots}$ be a partition of $\Omega$ such that $\map \Pr {B_i} > 0$ for each $i$.
Then:
- $\ds \expect X = \sum_i \expect {X \mid B_i} \, \map \Pr {B_i}$
whenever this sum converges absolutely.
In the above:
- $\expect X$ denotes the expectation of $X$
- $\expect {X \mid B_i}$ denotes the conditional expectation of $X$ given $B_i$.
Pages in category "Total Expectation Theorem"
The following 2 pages are in this category, out of 2 total.