Week 1: Revising probability: Axioms of probability, Conditional probability, Baye’s theorem, Random Variable, commonly used distributions (continuous and discrete), Cumulative Distribution Function (CDF) and Probability Density Function (PDF) their properties
Week 2: Revising probability: Joint distributions, Function of random variables. Independence of Random Variables, Correlation of Random Variables, Correlation coefficient, Markov and Chebyshev inequality, Convergence of RVs, Limit theorems.
Week 3: Introduction to python. Data visualization and fitting data to a given distribution.
Week 4: Exponential Family of Distributions, Population and Random Sampling, Sample mean, variance and standard deviation, Sampling from Normal distribution, Student’s t-distribution, F-distributions
Week 5: Order Statistics, Generating Random Samples: Direct and Indirect methods, Accept Reject method,
Week 6: Metropolis Hastings algorithm, Generation of random samples using Python
Week 7: Data reduction principles, Sufficiency principle, Sufficient statistics, factorization theorem
Week 8: Point estimators: Likelihood functions, maximum likelihood estimator, Method of moments, Bayes method, Expectation Maximization (EM) methods, Consistency of estimators
Week 9: Bias, Mean squared error, Evaluating Estimators, Cramer’s Rao inequality, Information inequality, Fischer Information
Week 10: Hypothesis testing, Likelihood Ratio Test (LRT), Type-I and Type-II errors, Method of Evaluating Tests
Week 11: Interval Estimators, Confidence intervals, Simple Linear regression, multivariate regression, logistic regression, Goodness of fit,
Week 12: p-test, Kolmogorov-Smirnoff test, f-score and other statistical tests. Application of tests on sample datasets using Python.