MA204

INTRODUCTION TO PROBABILITY THEORY

1. Definitions of Probability - Notion of sample space - Events - Basics of Combinatorial Analysis - Posing Probability problems mathematically - Examples
   
2. Conditional Probability - Baye's Rule - Random variable - Probability mass function, Density function, Distribution Function - Bernoulli Trials - Binomial Distribution - Poisson Approximation - Poisson Distribution - Normal Distribution - Moment Generating Function
   
3. Joint Probability Density Function - Marginal and Conditional Densities - Function of Random Variable - Covariance and Conditional Expectation - Correlation Coefficient
   
4. Chebyshev Inequality - Law of Large Numbers - Central Limit Theorem - Random Process - Markov Dependence, Markov Chains, definition, examples, ergodicity
   
5. Finite Markov Chain - Various States - Limiting Probability - Introduction to Markov Process - M/M/1 Queues with finite and infinite waiting space.
   

TEXT:

• W. FELLER, An Introduction to Probability Theory and its Applications, Vol. 1, Wiley Eastern, New Delhi.
• A. PAPOULIS, Probability, Random Variables and Stochastic Processes, McGraw Hill.
• K. S. TRIVEDI, Probability and Statistics with Reliability and Queueing and Computer Science Applications, Prentice Hall of India, 1988
• A. O. ALLEN, Introduction to Probability, Statistics and Queueing Theory with Computer Science Applications, Academic Press, 2006 reprint.