Probabilistic Analysis

Synonyms

Probability theory; Random processes; Random structures; Stochastic models; Uncertainty

Glossary

Asymptotically Almost Surely (a.a.s.):

The limit ℙ(E _n ) → 1 as n → ∞, where {E _n } denotes a sequence of events defined on a random structure (e.g., a random graph) that depends on n

Event:

A subset of the sample space

$\mathbb{G}\left( n, p\right)$ :

The probability space of simple random graphs that contain n vertices and for which each of the $\left(\begin{array}{c}\hfill n\hfill \\ {}\hfill 2\hfill \end{array}\right)$ edges occurs with probability p ∈ [0, 1]

Independent and Identically Distributed (i.i.d):

The hypothesis that some given random variables are mutually independent, and each is described by the same probability mass function

Probability Mass Function (p.m.f.):

A function that assigns a probability to the event that a random variable assumes a given value, e.g., p _X (x) = ℙ({ω ∈ Ω : X(ω) = x})

Probability Measure:

(ℙ) A function that assigns a probability...