Lecture 1 - Introduction to Probability
Lecture 2 - Consequences of Axioms
Lecture 3 - Interpretation of Probability
Lecture 4 - Total Probability law and Baye's Theorem - I
Lecture 5 - Total Probability law and Baye's Theorem - II
Lecture 6 - Random variables and Cumulative Density Function
Lecture 7 - Discrete and Continuous random variables - I
Lecture 8 - Discrete and Continuous random variables - II
Lecture 9 - Expectation and Variance
Lecture 10 - Function of Random variables
Lecture 11 - Generating RVs, Joint Distribution of RVs
Lecture 12 - Joint Distribution of RVs and Marginal densities
Lecture 13 - Covariance of Random variables
Lecture 14 - Moment Generating Functions
Lecture 15 - Conditional PMF and PDF
Lecture 16 - Law of Large numbers, Central Limit Theorem
Lecture 17 - Application of Central Limit Theorem - I
Lecture 18 - Application of Central Limit Theorem - II
Lecture 19 - Gamma and Chi-square distributions
Lecture 20 - Beta distributions and Exponential families
Lecture 21 - Random Sampling, Sample mean and Sample variance
Lecture 22 - Sampling from Gaussian distribution and t-distribution
Lecture 23 - Student's t- distribution
Lecture 24 - F-distribution and its properties
Lecture 25 - Convergence of Random variables and Consistency
Lecture 26 - Order statistics, Median and Percentiles
Lecture 27 - Generating random sample-Direct method
Lecture 28 - Generating random sample-Indirect method
Lecture 29 - Introduction to python
Lecture 30 - Python- Loops and Numpy library
Lecture 31 - Sufficiency Principles and Sufficient Statistics
Lecture 32 - Sufficient Statistics and Characterization of Sufficient Statistics
Lecture 33 - Characterization of Sufficient Statistics and Factorization Theorem
Lecture 34 - Example of Factorization Theorem, Minimal Sufficient Statistics
Lecture 35 - Minimal sufficient statistics
Lecture 36 - Test for minimal sufficient statistics withexamples, Ancillary Statistics
Lecture 37 - Likelihood Functions, Maximum Likelihood Estimator
Lecture 38 - Method of moments, Baye's Estimator
Lecture 39 - Evaluating Estimator, Cramer Rao Bound, Fisher Information
Lecture 40 - Evaluating Estimator, Cramer Rao Bound, Fisher Information (Continued...)
Lecture 41 - Hypothesis Testing, Likelihood Ratio Test
Lecture 42 - Hypothesis Testing, Bayes Test
Lecture 43 - Type I and II errors, Power Functions
Lecture 44 - Type I and II errors, Power Functions (Continued...)
Lecture 45 - Calculations of Power Functions
Lecture 46 - Unbiased Test, Uniformly Most Powerful Test,Neyman- Pearson Lemma, Interval Estimation
Lecture 47 - Interval Estimation
Lecture 48 - Interval Estimation (Continued...)
Lecture 49 - Constructiong Confidence Intervals from tests
Lecture 50 - Python- numpy and pandas functions II
Lecture 51 - Tutology of tests and confidence intervals
Lecture 52 - Tutology of tests and confidence intervals (Continued...)
Lecture 53 - p-value, p-test of significance of a statistical test
Lecture 54 - t-test and F-test, ANOVA
Lecture 55 - Non-parametric test, Goodness of fit, Chi- squared test
Lecture 56 - Distribution of Chi-squared test statistics
Lecture 57 - Kolmogrov-Smirnov test
Lecture 58 - Lilliefors's test and Explorator Data Analysis, Q-Q Plot and P-P Plot
Lecture 59 - Generating random samples using Python, Hypothesis Testing using Python
Lecture 60 - Generating random samples using Python, Hypothesis Testing using Python (Continued...)
