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
- $E \left({X}\right)$
Let $X$ be a discrete random variable.
The expectation of $X$ is written $E \left({X}\right)$, and is defined as:
- $\displaystyle E \left({X}\right) := \sum_{x \mathop \in \operatorname{Im} \left({X}\right)} x \Pr \left({X = x}\right)$
whenever the sum is absolutely convergent, that is, when:
- $\displaystyle \sum_{x \mathop \in \operatorname{Im} \left({X}\right)} \left|{x \Pr \left({X = x}\right)}\right| < \infty$
The $\LaTeX$ code for \(E \left({X}\right)\) is E \left({X}\right) .
Conditional Expectation
- $E \left({X \mid B}\right)$
Let $\left({\Omega, \Sigma, \Pr}\right)$ be a probability space.
Let $X$ be a discrete random variable on $\left({\Omega, \Sigma, \Pr}\right)$.
Let $B$ be an event in $\left({\Omega, \Sigma, \Pr}\right)$ such that $\Pr \left({B}\right) > 0$.
The conditional expectation of $X$ given $B$ is written $E \left({X \mid B}\right)$ and defined as:
- $\displaystyle E \left({X \mid B}\right) = \sum_{x \mathop \in \operatorname{Im} \left({X}\right)} x \Pr \left({X = x \mid B}\right)$
whenever this sum converges absolutely.
Note that $\Pr \left({X = x \mid B}\right)$ denotes the conditional probability that $X = x$ given $B$.
The $\LaTeX$ code for \(E \left({X \mid B}\right)\) is E \left({X \mid B}\right) .
