Course

Unit I

Review of probability concepts – conditional probability- Bayes theorem. Random Variable and Distributions: Introduction to random variable – discrete and continuous random variables and its distribution functions- mathematical expectations – moment generating function and characteristic function.

Unit II

Joint, marginal and conditional probability distributions for discrete and continuous cases, stochastic independence, expectation of two dimensional random variables, conditional mean and variance, correlation and introduction to regression.

Unit III

Standard distributions – Binomial, Multinomial, Poisson, Uniform, exponential, Weibull, Gamma, Beta, Normal. Mean, variance and applications of these distributions- Chebyshev’s theorem and central limit theorem.

Unit IV

Point estimation, properties, methods of estimating a point estimator, minimum risk estimators Sampling distributions of mean and variance, distributions of t, F and ChiSquare distribution. Central limit theorem.

Unit V

Interval estimation- Confidence interval for one mean, difference of two means, single proportion, difference of two proportions, single variance, ratio of two variances.

Course Outcomes:

CO1: Understand the basics of probability, random variables and distribution functions.

CO2: Know the importance of two dimensional random variables and correlation studies

CO3: Gain knowledge about standard statistical distributions and their properties

CO4: To gain knowledge point estimation and properties

CO5: To gain knowledge about sampling distributions interval estimations

Text Books /Reference Books:

1. Douglas C. Montgomery and George C. Runger, Applied Statistics and Probability for Engineers, John Wiley and Sons Inc., 2005.
2. Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye, Probability and Statistics for Engineers and Scientists, 8th Edition, Pearson Education Asia, 2007.
3. Ravichandran, J: Probability and Statistics for engineers, First Reprint Edition, Wiley India, 2012.
4. Hoel, P.G., Port, S.C., and Stone, C.J., Introduction to Probability Theory, Universal Book Stall, New Delhi, 1998