Details of MA2204 (Spring 2025)
| Level: 2 | Type: Theory | Credits: 3.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA2204 | Probability and Statistics II | Asok Kumar Nanda |
| Syllabus |
|---|
| Probability
Continuous random variables and density; discussion of special continuous distributions: uniform, normal, Cauchy, exponential, Laplace, gamma, beta along with their moments; moment generating function and its properties with some examples; functions of random variables; bivariate random variables with discussion of moments, covariance/correlation, independence and conditional distributions with examples of multinomial distribution and bivariate normal distribution;multivariate transformation of variables with examples of some sampling distributions for iid normal sample (chi-square, t and F, independence of sample mean and variance), large sample theory (convergence in probability and distribution including CLT and WLLN in iid case). Statistics: Descriptive statistics: Bivariate data and frequency distributions; scatter plot; correlation coefficient and regression lines; correlation index and correlation ratio, rank correlation coefficients. Inference: Brief overview of point estimation, hypothesis testing and confidence interval; some exact and approximate tests like tests relating to binomial, Poisson and normal distributions; Goodness of fit tests (if time permits) |
| References |
|---|
| Probabilty:
1. Cacoullos, T.; Exercises in Probability, Springer. 2. Feller, W.; An Introduction to Probability Theory and Its Applications, Vol. I, Wiley. 3. Gupta, S.C. and Kapoor, V.K.; Fundamentals of Mathematical Statistics, S. Chand. 4. Hoel, P.G., Port, S.C. and Stone, C.J.; Introduction to Probability Theory, Thomson Brooks/Cole. 5. Ross, S.; Introduction to Probability Models, Prentice-Hall. 6. Miller, I. and Miller, M., John E.; Freunds Mathematical Statistics with Applications, Pearson. Statistics: 7. Goon, A.M., Gupta, M. and Dasgupta, B.; Fundamentals of Statistics, Vols. I & II, World Press. 8. Miller, I. and Miller, M., John E.; Freunds Mathematical Statistics with Applications, Pearson. 9. Rencher, A.C.; Methods of Multivariate Analysis, Wiley. 10. Snedecor, G.W. and Cochran, W.G.; Statistical Methods. Iowa State University Press. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP | 4 | Not Allowed |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Not Allowed |
| 9 | MS | 4 | Core |
| 10 | MS | 6 | Not Allowed |
| 11 | MS | 8 | Not Allowed |
| 12 | RS | 1 | Not Allowed |
| 13 | RS | 2 | Not Allowed |