{{{credits}}}
| L | T | P | C |
| 4 | 0 | 0 | 4 |
- To provide a foundation on topics in applied probability and statistical methods needed for modern optimization methods and risk modeling.
- To address the issues and the principles of estimation theory, testing of hypothesis and multivariate analysis.
{{{unit}}}
| Unit I | Probability and Random Variables | 12 |
Random variables – Probability function – Moments – Moment generating functions and their properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions.
{{{unit}}}
| Unit II | Two Dimensional Random Variables | 12 |
Joint distributions – Marginal and conditional distributions – Transformation of two dimensional randomvariables – Correlation and regression
{{{unit}}}
| Unit III | Estimation Theory | 12 |
Unbiased estimators – Method of moments – Maximum likelihood estimation – Curve fitting by principle of least squares – Regression lines.
{{{unit}}}
| Unit IV | Testing of Hypothesis | 12 |
Large sample test based on Normal distribution for single mean and difference of means – Tests based on t, and F distributions for testing means and variances – Contingency table (Test for Independency) – Goodness of fit.
{{{unit}}}
| Unit V | Multivariate Analysis | 12 |
Random vectors and matrices – Mean vectors and covariance matrices – Multivariate normal density and its properties – Principal components – Population principal components – Principal components from standardized variables
\hfill Total: 60
After the completion of this course, students will be able to demonstrate competency in:
- Basic probability axioms and rules and the moments of discrete and continuous random variables (K3).
- Consistency, efficiency and unbiasedness of estimators, method of maximum likelihood estimation and Central Limit Theorem (K3).
- Use statistical tests in testing hypotheses on data (K3).
- Perform exploratory analysis of multivariate data, such as multivariate normal density, calculating descriptive statistics, testing for multivariate normality (K3).
- Use of the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools (K3).
- Devore J. L., “Probability and Statistics for Engineering and the Sciences”, 8th Edition, Cengage Learning, 2014.
- Dallas E. Johnson, “Applied Multivariate Methods for Data Analysis”, Thomson and Duxbury Press, 1998.
- Gupta S. C. and Kapoor V. K., “Fundamentals of Mathematical Statistics”, Sultan and Sons, New Delhi, 2001.
- Johnson R. A., Miller I. and Freund J., “Miller and Freund’s Probability and Statistics for Engineers”, Pearson Education, Asia, 8th Edition, 2015.
- Richard A. Johnson and Dean W. Wichern, “Applied Multivariate Statistical Analysis”, 5th Edition, Pearson Education, Asia, 2002.
| PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PO11 | ||
| K3 | K6 | K6 | K6 | K6 | ||||||||
| CO1 | K2 | 3 | ||||||||||
| CO2 | K3 | 3 | ||||||||||
| CO3 | K3 | 3 | ||||||||||
| CO4 | K3 | 3 | ||||||||||
| CO5 | K4 | 3 | ||||||||||
| Score | 15 | |||||||||||
| Course Mapping | 3 |