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Course Title: Mathematical Statistics Course Code: Credit Units: 4 Level: PG L T P/ S SW/F W TOTAL CREDIT UNITS 3 1 4 0 6 Please give your valuable feedback ratings (on the scale of 6 points) for following course curriculum with respect to relevance to Industry / Profession: 6 Excellent 5 Very Good 4 Good 3 Moderate 2 Needs Improvement # Course Title 1 Course Objectives: The main objective of the course is to provide the detailed knowledge of the random variable and its applications to various probability distributions. Also illustrate the use of basic statistical tools to analyze the given data and interpretation. 2 Prerequisites: NILL Student Learning Outcomes: 3 The students will be able to calculate moments, moment generating function characteristic function, random variables and distribution functions. The students will learn to get the solution of the problems based on probability distribution. The students will learn to get the solution of the problems based statistical inference. 4 1 Poor Feedback Rating (on scale of 6 points) The students will learn to get the solution of the problems based on correlation and regression. Course Contents / Syllabus: Module I Random variable and mathematical expectation 20% Weightage Set of events. Operation on sets, sequences of sets and their limits, Random variables and Distribution functions. Probability density function, Probability mass function. Mathematical Expectation, Expectation of a function of a random variable, conditional expectation, Moments of a random variable, variance and covariance of a random variable. Moment Generating function, Characteristic function, Probability generating function. 5 Module II Probability distributions 30% Weightage Discrete distributions: Bernoulli, Binomial, Poisson, Geometric, Negative Binomial, uniform, Hypergeometric and various properties. Computation mean and variance through moment generating function. Fitting of Binomial and Poission distribution. Continuous distributions: Uniform, exponential, Gamma distribution, Beta distribution, Normal distribution. Computation mean and variance through moment generating function. Fitting of Normal distribution. 6 Module III Statistical Inference 35% Weightage Introduction to statistical inference, Population, sample, parameter, Statistic and Estimator. Requirements of a good estimator: Unbiasedness, Consistency, Sufficiency, C.R. inequality and efficiency. Examples based on Normal, Binomial, Poisson, Geometric, Uniform, Exponential and Gamma distributions. Methods of Estimation: Method of Moments, Method of Maximum Likelihood .Test of significance based on Normal distribution, Student tdistribution, Test of single mean, difference of two means, Paired t-test, Chi-square, F-test and Analysis of variance (ANOVA) one way classification. 7 8 Module IV Regression Analysis 15% Weightage Scatter diagram, Correlation, types of correlation, Spearman’s rank correlation and properties of correlation. Linear Regression, lines of regressions and regression coefficients. Introduction of Partial and Multiple correlation and properties of residuals. Pedagogy for Course Delivery: 1. All the topics covered in the syllabus will be correlated with its applications in real life situations and also in other disciplines. 2. Extra sessions for revision will be undertaken. 11 Assessment/ Examination Scheme: Theory L/T (%) Lab/Practical/Studio (%) 30% End Term Examination NA Theory Assessment (L&T): Continuous Assessment/Internal Assessment Components (Drop Mid- 70% End Term Examination down) Weightage (%) Term Assignments Viva Attendance Exam 10% 7% 8% 5% 70% Text & References: 1. Feller,W.(1971): Introduction to Probability Theory and its Applications, Vol. I and II. Wiley Eastern-Ltd. 2. V. K. Rohatgi, (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern. 3. Hogg, R.V. and Craig, A.T.(1971): Introduction to Mathematical Statistics, McMillan. 4. Mood, A.M., Graybill,F.A. and Boes, D.C.(1974): Introduction to the Theory of Statistics, McGraw Hill. 6. Gupta and Kapoor (2013): Fundamentals of Mathematical Statistics, Sultan Chand and Sons Remarks and Suggestions: _______________________________ Date: Name, Designation, Organisation