MA204

INTRODUCTION TO PROBABILITY THEORY

Objectives

  • To introduce the fundamental concepts and theorems of probability theory
  • To apply elements of stochastic processes for problems in real life
  • To understand elementary queuing concepts and apply elsewhere in computer science.

 

Outcomes

  • Conceptualize the necessity of randomness concept in practical situation
  • Approximate the real problems using stochastic process and deduce results
  • Deduce useful results and interpret  them based on the analysis of queuing theory

 

Unit – I

            Axioms of probability theory- Probability spaces - Joint and conditional probabilities- Bayes’ Theorem- Independent events.

 

Unit – II

           Random Variable and random vectors -Distributions and densities. Independent random variables – Functions of one and two random variables. 

 

Unit – III

           Moments and characteristic functions- Inequalities of Chebyshev and Schwartz. Convergence concepts.

 

Unit – IV

          Random processes- Stationarity and ergodicity - Strict sense and wide sense stationary processes - Covariance functions and their properties - Spectral representation - Wiener-Khinchine theorem.

 

Unit – V

          Gaussian processes - Processes with independent increments - Poisson processes - Lowpass and Bandpass noise representations.

 

TEXT BOOKS

  • Davenport, Probability and Random Processes for Scientist and Engineers, McGraw-Hill
  • Papoulis, A., Probability, Random variables and Stochastic Processes, McGraw Hill.