21MAT317 PROBABILITY AND STATISTICS MATHEMATICS PAPER – VIII-
Unit I-
Probability Concepts: Sample Space and Events: Random Experiments – Sample Space – Events – Interpretations of Probability: Introduction – Axioms of probability – Addition Rules – Conditional Probability – Multiplication and Total Probability Rules – Independence – Bayes Theorem.
Unit II-
Discrete Random Variables and Distributions: Probability Mass Function – Cumulative Distribution Functions – Mean – Variance – Discrete Uniform Distribution – Binomial Distribution – Geometric and Negative Binomial Distribution – Poisson Distributions.
Unit III-
Continuous Random Variables and Distributions: Probability Density Functions – Cumulative Distribution Functions – Mean – Variance – Continuous Uniform Distribution – Exponential Distribution – Normal Distribution – Chebyshevs Inequality – Moment-Generating Functions.
Unit IV-
Two Dimensional Discrete and Continuous Random Variables: Joint Probability Distributions – Marginal Probability Distributions – Conditional Probability Distributions – Independence – Covariance and Correlation.
Unit V-
Point Estimation of Parameters: General Concept of Point Estimation – Methods of Point Estimation – Sampling distributions – Chi-square, t and F distributions (only definitions and use) – Central Limit Theorem.
Simple Linear Regression: Empirical Models – Simple Linear Regression
TEXTBOOKS:
REFERENCES:
- Ravichandran J., Probability and Statistics for engineers, 1st Reprint Edition, Wiley India, 2012.
- Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye, Probability and Statistics for Engineers and Scientists, 9th Edition, Pearson Education Asia, 2007.
- Sheldon M. Ross, Introduction to Probability and Statistical Inference, 6th edition, Pearson.
- A. Papoulis and Unnikrishna Pillai, Probability, Random Variable and Stochastic Processes, 4th edition, McGraw Hill, 2002.