Anna University , Chennai

Department of B.E-Electronics and Communication Engg

Probability and Random Processes

Units 1 , 2 , 4 and 5 Scanned Lecture Notes

Content :

Unit 1

Sample space

1.Trial and event

Exhaustive events

Mutually exclusive events

Favourable events

Equally likely events

Independent events

Mathematical defn. of probability

Axiomatic definition of probability

Openations on sets

Properties of sets

Complementary laws

Theorems on probability

Theorem 1

Theorem 2

Theorem 3

Theorem 4

Theorem 5

Theorem 6

Theorem 7

Conditional probability

Problems on conditional Probability

Baye’s theorem

Problems on Baye’s theorem

1.Discrete random variable

2.Probability mass function (prnf)

Probability distribution

2. Continuous random variable

Probability density function (pdf)

Expectation of X:-E:- (mean)

Cumulative distribution function (df)

Properties of the cumulative distribution function

Problems on continuous random variable

Moment generating function MGF

Moment generating function about origin

Properties of MGF

Unit 2

Standard distributions

Discrete distributions

Continuous distribution

1.Binomial distribution

Poisson distribution

Moment generating function of poisson distribution

Geometric distribution

Mean and variance of geometric distribution

Establish the memory loss property of Geometric distribution

Continuous distribution

Uniform distribution (or) Rectangular distribution

Gamma distribution

Additive property of Gamma distribution

Unit IV

Classification of random process

Introduction

Definition

Stationary Process

Average values of Random process

Strict sense stationary process ( SSS process )

Ergodic process

Definition

Marcov Process

Marcov chain

Transistion probability matrix:- (TPM)

Chapman Kolmogoron equation:- (CKE)

Initial probability dist

Normal process

Poisson process

Definition

Postulates

1.Independents

2.Homogeneity in time

3.Regularity

Theorem

Properties of poisson process

Additive property

Unit V

Correlation and Spectral Densities

Auto correlation and its properties

Properties of auto correlation fn.R©

Power spectral density function

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