Subject Code: MA2L003	Subject Name: Mathematics III (Probability, Statistics & Stochastic Processes)	L-T-P: 3-1-0	Credit: 4
Pre-requisite(s): Nil
Probability: Classical and axiomatic definitions of probability, Addition rule and conditional probability, Multiplication rule, Bayes' Theorem and independence, Discrete and continuous random variables: Uniform, Binomial, Geometric, Poisson, Exponential, Gamma, Normal distributions etc, Jointly distributed random variables. Mathematical expectation, Moments, Probability- and Moment-generating functions, Chebyshev's inequality, the strong and weak law of large numbers, Functions of Random Variables and their probability distributions Statistics: The Central Limit Theorem, Distributions of the sample mean and the sample variance for a normal population, Sampling Distributions: Chi-Square, t and F distributions, Point and interval Estimation, maximum likelihood estimation, Null and alternative hypotheses, The critical and acceptance regions, Neyman-Pearson Fundamental Lemma, Tests for one sample and two samples problems for normal populations. Stochastic Processes: Definition and classification of stochastic processes, Discrete time Markov chains, Random walk, Gambler’s ruin, Branching Processes, Time reversible Markov chains, Markov chain Monte Carlo methods, Poisson Process, Non-homogeneous and compound Poisson Process, General continuous time Markov chains, Birth and Death Process, Uniformization, Renewal process, Regenerative process, Semi Markov process, Application to queues, Brownian and stationary process. Text Books: Ross S. M. Introduction to Probability and Statistics for Engineers and Scientists, Academic Press Ross S.M. Stochastic Processes, Wiley Grimmett G. R.and Stirzaker D. R. Probability and Random Processes, Oxford University Press Reference Books: Hines W. W., Montgomery D. C., Goldsman D. M., Borror C. M. Probability and Statistics In Engineering, Wiley Taylor H.M. and Karlin S. An Introduction to Stochastic Modeling, Academic Press, New York Alon N. and Spenser J. Probabilistic Methods, John Wiley and Sons Bertsekas D. P. and Tsitsiklis J. N. Introduction To Probability, Athena Scientific

Subject Code: MA2L003

Subject Name: Mathematics III
(Probability, Statistics & Stochastic Processes)

L-T-P: 3-1-0

Credit: 4

Pre-requisite(s): Nil

Probability: Classical and axiomatic definitions of probability, Addition rule and conditional probability, Multiplication rule, Bayes' Theorem and independence, Discrete and continuous random variables: Uniform, Binomial, Geometric, Poisson, Exponential, Gamma, Normal distributions etc, Jointly distributed random variables. Mathematical expectation, Moments, Probability- and Moment-generating functions, Chebyshev's inequality, the strong and weak law of large numbers, Functions of Random Variables and their probability distributions
Statistics: The Central Limit Theorem, Distributions of the sample mean and the sample variance for a normal population, Sampling Distributions: Chi-Square, t and F distributions, Point and interval Estimation, maximum likelihood estimation, Null and alternative hypotheses, The critical and acceptance regions, Neyman-Pearson Fundamental Lemma, Tests for one sample and two samples problems for normal populations.
Stochastic Processes:
Definition and classification of stochastic processes, Discrete time Markov chains, Random walk, Gambler’s ruin, Branching Processes, Time reversible Markov chains, Markov chain Monte Carlo methods, Poisson Process, Non-homogeneous and compound Poisson Process, General continuous time Markov chains, Birth and Death Process, Uniformization, Renewal process, Regenerative process, Semi Markov process, Application to queues, Brownian and stationary process.
Text Books:

Ross S. M. Introduction to Probability and Statistics for Engineers and Scientists, Academic Press
Ross S.M. Stochastic Processes, Wiley
Grimmett G. R.and Stirzaker D. R. Probability and Random Processes, Oxford University Press

Reference Books:

Hines W. W., Montgomery D. C., Goldsman D. M., Borror C. M. Probability and Statistics In Engineering, Wiley
Taylor H.M. and Karlin S. An Introduction to Stochastic Modeling, Academic Press, New York
Alon N. and Spenser J. Probabilistic Methods, John Wiley and Sons
Bertsekas D. P. and Tsitsiklis J. N. Introduction To Probability, Athena Scientific