Course Details
Subject {L-T-P / C} : MA6621 : Probability and Statistics { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Suchandan Kayal
Syllabus
Probability: Classical, relative frequency and axiomatic definitions of probability, addition rule and
conditional probability, multiplication rule, total probability, Bayes’ Theorem and independence,
problems. Random Variables: Discrete and continuous random variables, probability mass,
probability density, and cumulative distribution functions, mathematical expectation, moments, moment
generating function, median, and quantiles, Chebyshev’s inequality. Special Distributions:
Discrete uniform, binomial, geometric, negative binomial, hypergeometric, Poisson, continuous uniform,
exponential, gamma, normal distributions. The function of a Random Variable: Distribution of function of a random variable. Joint Distributions: Joint, marginal, and conditional distributions, product moments,
correlation, independence of random variables.
Transformations: functions of random vectors, distributions of sums of random variables.
Sampling Distributions: The Central Limit Theorem, distributions of the sample mean and the sample
variance for a normal population, Chi-Square, t, and F distributions. Estimation: Unbiasedness,
consistency, the method of moments and the method of maximum likelihood estimation, confidence
intervals for parameters in one sample and two sample problems of normal populations, confidence
intervals for proportions, problems. Testing of Hypotheses: Null and alternative hypotheses, the critical
and acceptance regions, two types of error, power of the test, the most powerful test and Neyman Pearson Fundamental Lemma, tests for one sample and two sample problems for normal populations, tests for proportions, Chi-square goodness of fit test and its applications, problems.
Course Objectives
- This is a very basic course. Here, the students will learn fundamental theory and its applications to various real-life problems.
Course Outcomes
After this full course, the students will have a wide knowledge of the fundamental of probability and statistics. Indeed, they will be able to solve many real-life problems using the concepts of this course.
Essential Reading
- V. K. Rohatgi and A.K.Md.E. Saleh, An introduction to probability and statistics, Wiley , Second edition
- S M Ross, Introduction to Probability and Statistics for Engineers and Scientists, Academic Press
Supplementary Reading
- J.S. Milton & J.C. Arnold, Introduction to Probability and Statistics, Mc Graw Hill
- R. E. Walpole, R. H. Myers, S. L. Myers and K. Ye, Probability and Statistics for Engineers and Scientists, Pearson Education Inc.