INDEX

 

 

This page is an index for the commentaries and the notes.

 

 

 

A

 

Additive

-         countably

 

Aperiodic Markov chain

 

 

B

 

Balance equations

-         continuous time

-         discrete time

-         detailed in discrete or continuous time

 

Bayes, Thomas

            Bayes’ Rule

 

Bayesian Detection

 

Bernoulli, Jacob

 

Bernoulli Process

 

Brownian Motion Process

-         as scaled Bernoulli process

 

C

 

Cards – 52-card deck

 

Central Limit Theorem

-         Approximate

 

Chebychev Inequality

 

Classification of Markov chains

 

Communication Link

    - Optical

    - Wireless

Continuous – Probability

 

Confidence Intervals

 

Countable

-         Set

-         Additivity

 

Conditional

-         Probability

-         Expectation

o       Smoothing property

o       Of jointly Gaussian rvs

 

Continuous random variable

 

Convergence of random variables: see limits

 

Correlation

-         uncorrelation implies independence for jointly Gaussian rvs

 

D

 

De Moivre, Abraham

 

Detection

 

Digital communication link

Discrete random variable

 

E

 

Ergodicity

-         of random process

-         of Markov chain

 

Estimation

-         Properties of estimator

-         MMSE

-         LLSE

-         Recursive LLSE

 

 

Events

 

Expectation

-         Conditional

-         Of function of random variable

 

F

 

First passage time of Markov chain

 

Fortune process

 

Function

-         of random variable

-         of Markov process may not be Markov

 

G

 

Gambling system: Impossibility of

 

Gambler’s ruin problem

 

Gauss, Carl Friedrich

 

Gaussian random variables

- characteristic function

-         jointly

o       Conditional expectation of

o       Uncorrelated JG rvs are independent

-         moments

-         pdf

-         standard

 

Generating random variables

Generator

 

H

 

Holding time of state

 

Hypothesis Testing

                                                                     

I

 

Independent

-         Events

-         Random Variables

-         Pairwise but not mutually

 

Inequalities (Chebychev, Markov, Jensen)

 

Interpretation

-         of definitions

-         of probability as relative frequency

 

Irreducible Markov chain

 

J

 

Joint distribution

 

L

 

Laplace, Pierre Simon

 

Law of large numbers

-         weak

-         strong

 

Legendre, Adrien Marie

 

Limits of random variables

-         almost sure

-         criteria for convergence

-         in distribution

-         in L2

-         in probability

-         relationships

 

LLSE

-         recursive

 

M

 

Markov, Andrei Andreyevich

 

Markov

-         property of random process

-         chain (continuous time)

-         chain (discrete time)

-         inequality

 

Maximum a posteriori (MAP)

 

Maximum Likelihood Estimation (MLE)

 

Measurability

 

Memoryless Property

-         of Bernoulli process

-         of Poisson process

 

MMSE

-         see also

M/M/1 queue

Model

-         of uncertainty

 

Moments of random variable

 

N

 

Nonmeasureable sets

 

P

 

Paradox

-         Bertrand’s

-         Saint Petersburg for Bernoulli

-         Same for Poisson

-         Simpson’s

 

Periodic Markov chain

 

Poisson Process

-         as limit of Bernoulli

 

Probability space

 

R

 

Random

-         choosing at

-         function of outcome

-         process

-         variable

–        discrete

–        continuous

-         variables (collection)

–        limits

 

Rate matrix

 

Recurrent Markov chain

 

S

 

Scaling

-         Bernoulli: Brownian

-         Bernoulli: LLN

-         Bernoulli to Poisson

 

Simpson, Thomas

 

Simpson’s Paradox

 

Smoothing property of conditional expectation

 

Speech recognition

 

Stationary random process

 

Stationary Distribution

-         for continuous-time Markov chain

-         for discrete-time Markov chain

 

Stochastic Matrix

 

Strong Law of Large Numbers (SLLN)

 

Sufficient statistics

 

T

 

Time-reversibility

-         of random process

-         of discrete-time Markov chain

-         of continuous-time Markov chain

 

Transforms – example to show that binomial converges to Poisson

 

Transient Markov chain

 

Transition probability matrix

 

U

Uncertainty

-         versus model

 

VWw

 

Variance

 

Viterbi Algorithm

 

w - as the outcome of a random experiment

 

Weak Law of Large Numbers (WLLN)

 

Wiener Process

 

 

Jean Walrand – December 1999