Download Probability Random Process

With effect from Academic Year 2014-15
MT-221
PROBABILITY & RANDOM PROCESSES
Instruction
Duration of Semester-End Examination
Semester-End Examination
Sessional
Credits
4 periods per week
3 Hours
75 Marks
25 Marks
3
UNIT-I: BASIC PROBABILITY THEORY:
Basics: Definition of Probability, Sampling, Theorems in Probability.
Baye’s Theorem, repeated Trials, Bernoulli’s Theorem and Binomial Distribution.
UNIT-II: The Concepts of a Random Variable:Introduction, Types of random variables,distribution and density.
Functions,
conditional
distribution,
Approximation
of
Binomial
Random
Variable.Transformation of random variables,Function of one dimensional random variable:The
random variable g(x), the distribution of g(x), Mean, Variance, Moments, Moment generating
function (MGF), Cumulative generating function (CGF) & Characteristic function (CF).
UNIT-III : TWO RANDOM VARIABLES:Bi-variant distribution ,one function of two random variables,
Two functions of two random variables .
Joint Moments ,Joint Characteristic functions ,conditional expection.
UNIT – IV : RANDOM PROCESSES:Definition, Basic concepts and examples, StationarityandErgodicity.
Second order process, Weakly stationary processes, co-variance functions and their properties.
Special representation.Weiner –Kin chine Theorem.
UNIT-V: LINEAR OPERATIONS :Noise, Poisson Processes, Gaussian process, properties of Gaussian process, filters, Low passfilter and Band pass-filter and Noise representation
Books:
1. T.Veerarajan
“Probability, Random Variable and Random Process”
Tata McGraw Hill Education Private Limited Third Edition
2. Papoulis
“Probability , Random variable and Stochastic Process”
Tata McGraw Hill Education Private Limited Fifth Edition
3. A.M.Natarajan,A.Tamilarasi “Probability Random Process and Queueing Theory”,New Age
International Publishers.
4. S.C.Gupta&V.K.Kapoor, “Fundamentals of Mathematical Statistics”
(S.Chand Publishers.