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$\mathrm E$

The Système Internationale d'Unités metric scaling prefix denoting $10^{\, 18 }$.

Its $\LaTeX$ code is \mathrm {E} .


$\mathrm E$ or $\mathrm e$

The hexadecimal digit $14$.

Its $\LaTeX$ code is \mathrm E  or \mathrm e.




Used by some authors to denote a general set.

The $\LaTeX$ code for \(E\) is E .

Identity Element


Used to indicate the identity element in a general algebraic structure.

If $e$ is the identity of the structure $\left({S, \circ}\right)$, then a subscript is often used: $e_S$.

This is particularly common when more than one structure is under discussion.

The $\LaTeX$ code for \(e_S\) is e_S .


Euler's number


Euler's number $e$ is the base of the natural logarithm $\ln$.

$e$ is defined to be the unique real number such that the value of the (real) exponential function $e^x$ has the same value as the slope of the tangent line to the graph of the function.

The $\LaTeX$ code for \(e\) is e .



$\mathcal E$

An experiment, which can conveniently be denoted $\mathcal E$, is a measure space $\left({\Omega, \Sigma, \Pr}\right)$ such that $\Pr \left({\Omega}\right) = 1$.

The $\LaTeX$ code for \(\mathcal E\) is \mathcal E .


$\operatorname E \paren X$

Let $X$ be a discrete random variable.

The expectation of $X$ is written $\operatorname E \paren X$, and is defined as:

$\expect X := \displaystyle \sum_{x \mathop \in \image X} x \Pr \paren {X = x}$

whenever the sum is absolutely convergent, that is, when:

$\displaystyle \sum_{x \mathop \in \image X} \size {x \Pr \paren {X = x} } < \infty$

The $\LaTeX$ code for \(\operatorname E \paren X\) is \operatorname E \paren X .

Conditional Expectation

$\operatorname E \paren {X \mid B}$

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 $\Pr \paren B > 0$.

The conditional expectation of $X$ given $B$ is written $\operatorname E \paren {X \mid B}$ and defined as:

$\displaystyle \operatorname E \paren {X \mid B} = \sum_{x \mathop \in \image X} x \Pr \paren {X = x \mid B}$


$\Pr \paren {X = x \mid B}$ denotes the conditional probability that $X = x$ given $B$

whenever this sum converges absolutely.

The $\LaTeX$ code for \(\operatorname E \paren {X \mid B}\) is \operatorname E \paren {X \mid B} .