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Syllabus

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.

Text Books

  • Douglas C. Montgomery and George C.Runger, Applied Statistics and Probability for Engineers, (2005) John Wiley and Sons Inc

Resources

  • 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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