Course Archives Documentation Research and Training Centre Unit | |||||
Course: Elements of Mathematics and Statistics Level: Postgraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: Module 1: Elements of Mathematics Unit 01: Set theory: Sets and their representation; Universal Set; Empty Set; Subsets; Power Setâ€™ Venn Diagrams; Union and Intersection of Sets; Difference of Sets; Complements of Sets Unit 02: Relations and Functions: Ordered pairs, Definition of a relation, domain and range of a relation; Functions as a special kind of relation from one set to another, domain and range of a function, real valued functions of the real variable, graphs of standard functions One to one and onto functions, inverse of a function, composite functions Module 2: Introduction to Statistics Unit 03: Introduction to Statistics Unit 04: Statistical Applications, Challenges Module 3: Data Collection and Presentation Unit 05: Methods of data collection; Scales of measurement Unit 06: Data Pre-processing: Coding, Classification, Tabulation etc Unit 07: Data Visualisation - graphical and tabular; Frequency tables and curves, histogram, Frequency Polygon, Ogive etc Module 4: Descriptive Statistics Unit 08: Measures of central tendency Unit 09: Measures of Dispersion Unit 10: Measures of Asymmetry Unit 11: Measures of Relationship Unit 12: Simple Regression, Regression Vs Correlation Unit 13: Index and Time Series Module 5: Basics of Probability Unit 14: Probability: Concepts: Classical and axiomatic, Unit 15: properties of a probability measure; conditional probability, etc Module 6: Independent events and Random variable Unit 16: Independent events, random variable, discrete and continuous random variable Unit 17: Distribution function, probability density functions Unit 18: Probability Distributions such as Normal, Exponential, Binomial, Poisson, Geometric, Negative binomial distributions Module 7: Statistical Test, Analysis of Variance and Regression analysis Unit 19: Confidence intervals Unit 20: Estimatiend Parameters Unit 21: T-Test Unit 22: Z-Test Unit 23: Chi - Square tests, Goodness-of-fit test Unit 24: Analysis of Variance (ANOVA) and Unit 25: Analysis of Covariance (ANCOVA) Unit 26: Regression analysis; Curve fitting Module 8: Practicals Unit 27-29: Statistical tests and regression analysis Unit 30-32: Introduction to statistical analysis tool (such as R) Reference Texts: 1. David M. Dietz, Christopher D. Barr, and Mine Cetinkaya-Rundel (2015). OpenIntro Statistics, American Institute for Mathematics. 2. Mathematics Class 11th textbook. NCERT. 3. Nicholas J. Horton, Daniel T. Kaplan, and Randall Pruim (2015). A Studentâ€™s Guide to R. 4. Freedman, David, Robert Pisani, & Roger Pervis (2007). Statistics. New York: W. W. Norton. 5. James, Gareth, Daniela Witten, Trevor Hastie, & Robert Tibshirani (2013). An Introduction to Statistical Learning: With Applications in R. New York: Springer. 6. Kabacoff, Robert (2015). R In Action: Data Analysis and Graphics with R. Shelter Island, NY: Manning Publications Co. Top of the page Past Exams | |||||
Midterm
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[Indian Statistical Institute] |