Symbols:E
Contents
exa-
- $\mathrm E$
The Système Internationale d'Unités metric scaling prefix denoting $10^{\, 18 }$.
Its $\LaTeX$ code is \mathrm {E} .
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: Entry: E (5)
Hexadecimal
- $\mathrm E$ or $\mathrm e$
The hexadecimal digit $14$.
Its $\LaTeX$ code is \mathrm E or \mathrm e.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: Entry: E
Set
- $E$
Used by some authors to denote a general set.
The $\LaTeX$ code for \(E\) is E .
Identity Element
- $e$
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 .
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: Entry: e (2)
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 .
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: Entry: e (1)
Experiment
- $\mathcal E$
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 .
Expectation
- $\operatorname E \paren X$
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:
- $\displaystyle \operatorname E \paren {X \mid B} = \sum_{x \mathop \in \image X} x \Pr \paren {X = x \mid B}$
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 \(\operatorname E \paren {X \mid B}\) is \operatorname E \paren {X \mid B} .
