Engineering Statistics

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.