Title-Probability Distributions (Code-09050305)
B.Sc. (Hons) Mathematics (4th semester)
S.No. | Contents of the topics | Learning Objectives | Teaching Guidelines | Methodology | Time
(Hour) |
1 | · Generating functions: Moment generating function and cumulant generating function along with their properties and uses
· Chebychev’s inequality · Convergence in probability · Weak and strong laws of large numbers(Statements only) |
Students will be able to understand Study of MGF and inequalities | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 10 |
2 | · Bernoulli Distribution
· Binomial Distribution · Poisson Distribution · Geometric and hyper-geometric distributions · Properties of all above distributions |
Students will be able to understand Study of distributions with their properties | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 15 |
3 | · Uniform, gamma, beta(first and second kinds) distributions
· Exponential distributions · Properties of all above distributions |
Students will be able to understand Study of distributions with their properties | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 12 |
4 | · Normal distribution with its properties
· Central Limit Theorem (Statement only) · Applications of CLT |
Students will be able to understand Study of CLT and its applications | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 12 |
Books Recommended:
- Baisnab and M. Jas, Element of Probability and Statistics, Tata McGraw Hill.
- L.Meyer, Introductory Probability and Statistical Applications, Addison-Wesley Publishing Company, 1970.
- C. Gupta and V.K. Kapoor, Fundamentals of Mathematical Statistics, Sultan Chand & Sons, 2002.