Probability and Random Processes (Units 1,2 , 4 and 5) Scanned Lecture Notes

[Srini]

   

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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