Probability, Statistics and Linear Programming

Course Objectives:

1. To understand probability and probability distributions.
2. To understand methods of summarization of data.
3. To understand and use test for hypothesis.
4. To understand methods for solving linear programming problems.

Course Outcomes (CO):

• CO1: Ability to solve probability problems and describe probability distributions.
• CO2: Ability to describe and summarize data.
• CO3: Ability to use test for hypothesis.
• CO4: Ability to formulate and solve linear programming problems.

Unit I

Basics: Probability and Statistical models, Sample Spaces and Events, Counting Techniques, Interpretations and Axioms of Probability, Unions of Events and Addition Rules, Conditional Probability, Intersections of Events and Multiplication and Total Probability Rules, Independence, Bayes’ Theorem, Random Variables.

Discrete and Continuous Random Variables and Distributions: Probability Distributions and Probability Mass /density Functions, Cumulative Distribution Functions, Mean and Variance of a Random Variable, Discrete and continuous Uniform Distribution, Binomial Distribution, Geometric and Negative Binomial Distributions, Hypergeometric Distribution, Poisson Distribution. Normal Distribution, Normal Approximation to the Binomial, and Poisson Distributions; Exponential Distribution, Erlang and Gamma Distributions, Weibull Distribution, Lognormal Distribution, Beta Distribution.

Unit II

Joint Probability Distributions for Two Random Variables, Conditional Probability Distributions and Independence, Joint Probability Distributions for Two Random Variables, Covariance and Correlation, Common Joint Distributions, Linear Functions of RandomVariables, General Functions of Random Variables, Moment- Generating Functions.

Numerical Summaries of Data, Stem-and-Leaf Diagrams, Frequency Distributions and Histograms, Box Plots, Time Sequence Plots, Scatter Diagrams, Probability Plots. Point Estimation, Sampling Distributions and the Central Limit Theorem without proof, General Concepts of Point Estimation, Methods of Point Estimation, Statistical Intervals for a Single Sample.

Unit III

Hypotheses Testing for a SingleSample: Tests on the Mean of a Normal Distribution with Variance Known / Unknown, Tests on the Variance and Standard Deviationof a Normal Distribution, Tests on a Population Proportion, Testing for Goodness of Fit, Nonparametric tests (Signed, Wilcoxon), Similarly Statistical Inference for Two Samples.

Regression and Correlation: Linear Regression, Least Squares Estimators, Hypotheses testing for simple linear regression, Confidence Intervals, Adequacy of model, Correlation, Transformed Variables, Logistic Regression. Similarly, for multiple linear regression including aspects of MLR.

Unit IV

Linear Programming: Introduction, formulation of problem, Graphical method, Canonical and Standard form of LPP, Simplex method, Duality concept, Dual simplex method, Transportation and Assignment problem.

Textbooks:

1. Applied Statistics and Probability for Engineers by Douglas G. Montgomery and Runger, Wiley, 2018
2. Linear Programming by G. Hadley, Narosa, 2002

References:

1. Miller and Freund’s Probability and Statistics for Engineers by Richard A. Johnson, Pearson, 10th Ed., 2018.
2. Probability & Statistics for Engineers & Scientists by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye, Pearson, 2016.
3. Statistics and probability with applications for engineers and scientists using Minitab, R and JMP, C. Gupta, Irwin Guttman, and Kalanka P. Jayalath, Wiley, 2020.
4. Probability and Statistics for Engineering and the Sciences, Jay Devore, Cengage Learning, 2014.
5. Probability and Statistics in Emgineering, William W. Hines, Douglas C. Montgomery, David M. Goldman, and Connie M. Borror, Wiley, 2003.
6. Operations Research: An Introduction by Hamdy A. Taha, Pearson, 10th Edition, 2016