# Symbols:E

## Contents

## 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}`

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## Hexadecimal

- $\mathrm E$ or $\mathrm e$

The hexadecimal digit $14$.

Its $\LaTeX$ code is `\mathrm E`

or `\mathrm e`

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## Set

- $E$

Used by some authors to denote a general set.

The $\LaTeX$ code for \(E\) is `E`

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## 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`

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## 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`

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## 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`

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## 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`

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## 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}`

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## 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`

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