Symbols:Abbreviations/P

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P

PBD

Pairwise balanced design.

PCI

Principle of Complete Induction (or Principle of Complete Finite Induction).

PCFI

Principle of Complete Finite Induction.

PDE

Partial differential equation.

A partial differential equation is a differential equation which has:

one dependent variable

more than one independent variable.

The derivatives occurring in it are therefore partial.

pdf

Probability density function:

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be an absolutely continuous random variable on $\struct {\Omega, \Sigma, \Pr}$.

Let $P_X$ be the probability distribution of $X$.

Let $\map \BB \R$ be the Borel $\sigma$-algebra of $\R$.

Let $\lambda$ be the Lebesgue measure on $\struct {\R, \map \BB \R}$.

We define the probability density function $f_X$ by:

$\ds f_X = \frac {\d P_X} {\d \lambda}$

where $\dfrac {\d P_X} {\d \lambda}$ denotes the Radon-Nikodym derivative of $P_X$ with respect to $\lambda$.

PERT

Program Evaluation and Review Technique.

PET

Principle of the Excluded Third.

PFI

Principle of Finite Induction.

PGF or p.g.f.

Probability generating function:

Let $X$ be a discrete random variable whose codomain, $\Omega_X$, is a subset of the natural numbers $\N$.

Let $p_X$ be the probability mass function for $X$.

The probability generating function for $X$, denoted $\map {\Pi_X} s$, is the formal power series defined by:

$\ds \map {\Pi_X} s := \sum_{n \mathop = 0}^\infty \map {p_X} n s^n \in \R \sqbrk {\sqbrk s}$

PID or pid

Principal ideal domain:

A principal ideal domain is an integral domain in which every ideal is a principal ideal.

PMF, pmf or p.m.f.

Probability mass function:

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X: \Omega \to \R$ be a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.

Then the probability mass function of $X$ is the (real-valued) function $p_X: \R \to \closedint 0 1$ defined as:

$\forall x \in \R: \map {p_X} x = \begin{cases}

\map \Pr {\set {\omega \in \Omega: \map X \omega = x} } & : x \in \Omega_X \\ 0 & : x \notin \Omega_X \end{cases}$ where $\Omega_X$ is defined as $\Img X$, the image of $X$.

That is, $\map {p_X} x$ is the probability that the discrete random variable $X$ takes the value $x$.

PMI

Principle of Mathematical Induction.

PNT

Prime Number Theorem.

Poset

Partially Ordered Set.

A partially ordered set is a relational structure $\struct {S, \preceq}$ such that $\preceq$ is a partial ordering.

The partially ordered set $\struct {S, \preceq}$ is said to be partially ordered by $\preceq$.

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