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} .


Hexadecimal

$\mathrm E$ 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)

Definition:East (Celestial)

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