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:

  1. Douglas C. Montgomery and George C. Runger, Applied Statistics and Probability for Engineers, 3rd edition, John Wiley and Sons Inc., 2005

REFERENCES:

  1. Ravichandran J., Probability and Statistics for engineers, 1st Reprint Edition, Wiley India, 2012.
  2. 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.
  3. Sheldon M. Ross, Introduction to Probability and Statistical Inference, 6th edition, Pearson.
  4. A. Papoulis and Unnikrishna Pillai, Probability, Random Variable and Stochastic Processes, 4th edition, McGraw Hill, 2002.