Syllabus (MATHEMATICS)
Course Type: MAJ-9
Semester: 6
Course Code: BMTMMAJ09T
Course Title: Probability & Statistics
(L-P-Tu): 5-0-1
Credit: 6
Practical/Theory: Theory
Course Objective: To be done.
Learning Outcome: Course Outcomes (CO): The whole course will have the following outcomes: Upon successful completion of this course, students will be able to CO1: calculate the expectation and moments of one and two dimensional random variables. CO2: use of some important
Syllabus:
Unit -1: Probability [Credit: 3, 45L]
- Sample space and Axiomatic definition of probability, Compound experiment.
- One and two dimensional random variables (Discrete and Continuous): Distribution function and its basic properties, Probability density function, Marginal distribution and density function, Conditional density function.
- Transformation of one and two dimensional random variables.
- Mathematical expectation, Median, Mode, Moments, Variance.
- Expectation for two dimensional case, Moments, Covariance, Correlation coefficient and its properties, Addition and multiplication rule for expectation and variance, Independent random variables. Moment generating function, Characteristic function.
- Conditional expectation and regression – Least square regression lines and basic properties.
- Some important distributions: Binomial, Poisson, Uniform, exponential, Cauchy, Normal, Gamma, Beta and their basic property.
- Tchebycheff’s inequality, Convergence in probability, Bernoulli’s limit theorem, Central limit theorem.
- Approximations – Binomial to Poisson, Central limit theorem (statement only). Binomial to Normal ( De Moivre-Laplace limit theorem)
Unit -2: Statistics [Credit: 2, 30L]
- Concept of statistics, Sampling distribution of sample mean for finite population with examples.
- Sampling distribution for infinite population, Exact sampling distribution-for mean of normal population, Chi-square and t-distribution.
- Point Estimation – consistent, unbiased, MVUE. Method of maximum likelihood and application to different population.
- Interval estimation- Method of finding confidence interval- Application to normal population
- Testing of hypothesis: Critical region, Type-I and Type-II error, Power of test, Large sample test related to Binomial proportion, Chi-square test on multinomial distribution, Exact tests for mean and variance of univariate Normal distribution.
Reading References:
- A.P. Baisnab and M. Jas; Elements of Probability and Statistics ; Tata McGraw Hill Co. Ltd
- Amritava Gupta; Groundwork of Mathematical Probability and Statistics; Academic Publishers.
- Gun, Gupta, Dasgupta; Fundamentals of Statistics; World Press.
- S.C. Gupta, V .K. Kapoor; Fundamentals of Mathematical Statistics; S Chand & Sons.
- N.G. Das; Statistical Methods; M Das & Co.
Basic Features
Undergraduate degree programmes of either 3 or 4-year duration, with multiple entry and exit points and re-entry options, with appropriate certifications such as:
- UG certificate after completing 1 year (2 semesters with 40 Credits + 1 Summer course of 4 credits) of study,
- UG diploma after 2 years (4 semesters with 80 Credits + 1 Summer course of 4 credits) of study,
- Bachelor’s degree after a 3-year (6 semesters with 120 credits) programme of study,
- 4-year bachelor’s degree (Honours) after eight semesters (with 170 Credits) programme of study.
- 4-year bachelor’s degree (Honours with Research) if the student completes a rigorous research project (of 12 Credits) in their major area(s) of study in the 8th semester.
Note: The eligibility condition of doing the UG degree (Honours with Research) is- minimum75% marks to be obtained in the first six semesters.
- The students can make an exit after securing UG Certificate/ UG Diploma and are allowed to re-enter the degree programme within three years and complete the degree programme within the stipulated maximum period of seven years.
