|Probability and Statistics||Learning Schedule|
|Pre-requisites: Basic Mathematics||3||0||0||3|
Introduction to the fundamental ideas and techniques of probability theory and statistical inference.
COURSE OBJECTIVES :
- To give an exposure to the students the basic concepts of Probability and Statistical methods and their application.
- To serve as a foundation to analyze problems in Science and Engineering applications through Statistical testing Method.
COURSE OUTCOMES :
On completion of this course, the students are expected to learn Basics of Probability distributions, Sampling theory and Theory of Estimation Various tests of Hypothesis and Significance, Correlation and Regression and fitting of different types of curves .
COURSE CONTENT :
Unit I: Probability Distributions
Review of basic probability, Random variables, Probability Distribution, Mathematical Expectation and Variance of Probability distribution, Standard discrete distributions: Binomial, Poisson and Geometric distributions, Probability density function, Cumu-lative distribution function, Expectation and Variance, Standard continuous distributions – Uniform, Normal, Exponential, Joint distribution and Joint density functions
Unit II: Sampling Theory
Population and Sample, Statistical inference, Sampling with and without replacement, Random samples, Population parameters, Sample statics, Sampling distributions, Sample mean, Sampling distribution of means, Sample variances, Sampling distribution of variances, Case where population variances is unknown, Unbiased estimates and efficient estimates, point estimate and Interval Estimates, Confidence Interval estimates of population parameters, Confidence intervals for variance of a Normal distribution, Maximum likelihood estimates.
Unit III: Tests of Hypothesis and Significance
Statistical hypothesis, Null and Alternate hypothesis, test of hypothesis and significance, Type I and Type II errors, Level of Sig-nificance, Tests involving the Normal distribution, One-Tailed and Two-Tailed tests, P value. Special tests of significance for Large samples and Small samples (F, chi- square, z, t- test), ANOVA.
Unit IV: Correlation and Regression
Correlation, Rank correlation, Regression Analysis, Linear and Non linear Regression, Multiple regression, Curve fitting by meth-od of least squares, fitting of straight lines, polynomials, exponential curves.
- E. Walpole, R. H. Mayers, S. L. Mayers and K. Ye, (2007), Probability and Statistics for Engineers and Scientists,8th Edition, Pearson Education, ISBN: 978-8-131-71552-9.
- Sheldon M. Ross, (2011), Introduction to Probability and Statistics for Engineers and Scientists, 4th Edition, Academic Foundation, ISBN: 978-8-190-93568-5.
- Douglas C. Montgomery, (2012), Applied Statistics and Probability for Engineers, 5th Edition, , Wiley India, ISBN: 978-8-126-53719-8.
- Spiegel, M. R., Schiller, J. and Srinivasan, R. A., (2010), Probability & Statistics, 3rdEdition, TataMcGraw Hill, ISBN : 978-0-070-15154-3.