'Probability and Statistics' is a course offered in the B. Tech. programs at School of Engineering, Amrita Vishwa Vidyapeetham.
Unit 1
Probability Concepts: Review of probability concepts - Bayes’ Theorem.
Random Variable and Distributions: Introduction to random variable – discrete and continuous distribution functions - mathematical expectations – moment generating functions and characteristic functions. Binomial, Poisson, Geometric, Uniform, Exponential, Normal distribution functions (MGF, mean, variance and simple problems) – Chebyshev’s theorem.
Unit 2
Sampling Distributions: Distributions of Sampling Statistics, Chi-square, t and F distributions (only definitions and use). Central Limit Theorem.
Theory of estimation: Point Estimation, Unbiased estimator - Maximum Likelihood Estimator - Interval Estimation.
Unit 3
Testing of Hypothesis: Large and small sample tests for mean and variance – Tests based on Chi-square distribution.
- Douglas C. Montgomery and George C.Runger, Applied Statistics and Probability for Engineers, (2005) John Wiley and Sons Inc
- J. Ravichandran, “Probability and Random Processes for Engineers”, First Edition, IK International, 2015.
- Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye, Probability and Statistics for Engineers and Scientists, 8th Edition (2007), Pearson Education Asia.
- Sheldon M Ross, Introduction to Probability and Statistical Inference, 6th Edition, Pearson.
- A. Papoulis, and Unnikrishna Pillai, “Probability, Random Variables and Stochastic Processes”, Fourth Edition, McGraw Hill, 2002.
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