EECS 126 - Probability and Random Processes - J. Walrand

INDEX

 K O Q XY Z

A

-         countably

B

Balance equations

-         continuous time

-         discrete time

-         detailed in discrete or continuous time

Bayes, Thomas

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

Continuous – Probability

Confidence Intervals

Countable

-         Set

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

Discrete random variable

E

Ergodicity

-         of random process

-         of Markov chain

Estimation

-         Properties of estimator

-         MMSE

-         LLSE

-         Recursive LLSE

Events

-         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

-         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

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)

Measurability

Memoryless Property

-         of Bernoulli process

-         of Poisson process

MMSE

M/M/1 queue

Model

-         of uncertainty

Moments of random variable

N

Nonmeasureable sets

P

-         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

Smoothing property of conditional expectation

Speech recognition

Stationary random process

Stationary Distribution

-         for continuous-time Markov chain

-         for discrete-time Markov chain

Stochastic Matrix

Sufficient statistics

T

Time-reversibility

-         of random process

-         of discrete-time Markov chain

-         of continuous-time Markov chain

Transient Markov chain

Transition probability matrix

U

Uncertainty

-         versus model

VWw

w - as the outcome of a random experiment

Wiener Process

Jean Walrand – December 1999