A First Course in Probability and Markov Chains

Index

algebra, 35

events, 35

algorithm

Hastings–Metropolis, 230

Bernoulli

distribution, 42, 46

process

finite, 41, 295

infinite, 44, 45, 95, 103, 151, 296

Bernstein polynomials, 152

binary sequences, 45

infinite Bernoulli process, 46, 103

binomial

coefficient, 1

generalized binomial, 3

series, 3

cardinality

denumerable, 45

multiplicity function, 62

of the continuum, 45

of the set of

derangements, 9, 63

functions, 12

lists, 11

multisets, 11

permutations, 8, 9

subsets, 8

central limit, 160

continuity correction, 163

uniform bound, 161

uniform convergence, 161

coefficient

binomial, 1

correlation, 123

generalized binomial, 3

multinomial, 20

collocations of objects

identical, 22

multiplicative property, 23

multiplicity function, 22

pairwise distinct, 19–21

grouping map, 19

multiplicative property, 23

conditional probability, 51

Bayes, 52

multiplication formula, 51

transition probabilities, 174

continuous semigroup, 250, 321

differentiability, 322, 323

exponential of a matrix, 321

infinitesimal generator, 250, 322

intensities matrix, 250

matrix exponential, 250

convergence

almost everywhere, 298–300

almost sure, 143–5, 159, 166

in , 143

in law, 159, 308, 310

in measure, 298–300

in probability, 143

weak of measures, 160, 308

counting process, 158

covariance, 121

density

mass, 41, 43

of the sum, 130

with respect to the Lebesgue measure, 73

derangement, 9

derivative of the determinant, ...