Syllabus
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Course Code: Elective 2 MMATH21 -310 Course Name: Mathematical Statistics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Measures of central tendency, measures of dispersion, measures of skewness, measures of Kurtosis. Probability-Basic terminology, addition theorem of probability, Boole’s inequality, conditional probability, Multiplication theorem of probability, independent events. Bayes’ theorem. Distribution function, discrete random variable, continuous random variable, two dimensional random variable, transformation of one dimensional random variable, transformation of two dimensional random variable. | |
| 2 | Mathematical expectation, expectation of random variable, expectation of function of random variable, properties of expectation and variance , Covariance, Cauchy-schwarz inequality, Jenson inequality, moment generating function, cumulants, characteristic function, Chebychev’s Inequality, convergence in probability, weak law of large numbers, scatter diagram, karl pearson’s coefficients of Correlation, Linear regression | |
| 3 | Discrete probability distributions-uniform distributions, Bernoulli distributions, Binomial distributions, Poisson distributions. Continuous probability distribution- Normal distributions, rectangular distributions, triangular distributions, Gamma distributions. Central limit theorem. Sampling distributions- chi square distribution, Student’s ‘t’ distribution, F distribution, relation between t and F , relation between F and chi-square. | |
| 4 | Large sample theory- types of sampling, parameter and statistic, test of significance, procedure for testing of hypothesis. Statistical inference- characteristic of estimators, Cramer-Rao inequality, MVU, Rao-Blackwell theorem. | |
