# Symbols:E

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## exa-

$\mathrm E$

The Système Internationale d'Unités symbol for the metric scaling prefix exa, denoting $10^{\, 18 }$, is $\mathrm { E }$.

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

$\mathrm E$ or $\mathrm e$

The hexadecimal digit $14$.

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

## Set

$E$

Used by some authors to denote a general set.

The $\LaTeX$ code for $E$ is E .

## Identity Element

$e$

Denotes the identity element in a general algebraic structure.

If $e$ is the identity of the structure $\struct {S, \circ}$, 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

$e$

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 .

## Experiment

$\mathcal E$

An experiment, which can conveniently be denoted $\EE$, is a measure space $\struct {\Omega, \Sigma, \Pr}$ such that $\map \Pr \Omega = 1$.

The $\LaTeX$ code for $\mathcal E$ is \mathcal E  or \EE.

## Expectation

$\expect X$

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 $\expect X$ is \expect X .

## 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 $\Pr \paren B > 0$.

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

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

where:

$\Pr \paren {X = x \mid B}$ 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} .

## East

$\mathrm E$

### East (Terrestrial)

East is the direction on (or near) Earth's surface along the small circle in the direction of Earth's rotation in space about its axis.

### East (Celestial)

The $\LaTeX$ code for $\mathrm E$ is \mathrm E .