IIT Madras Stats 2 Lectures: Statistics for Data Science II
BSMA1004119 lectures12 weeks
Weeks
- Week 17 lecturesJoint PMF of two discrete random variables · Marginal PMF of discrete random variables · Conditional distribution of one random variable given another · Examples on joint, marginal and conditional probabilities · Joint PMF of more than two discrete random variables · Marginal PMF of multiple discrete random variables · Conditioning with multiple discrete random variables
- Week 211 lecturesIndependence of two random variables · Independence of multiple random variables · Visualizing functions of one random variable, one-to-one functions · Visualizing functions of one random variable, many-to-one functions · Examples on functions of one random variable | probability mass function · Introduction to functions of two random variables · Sum of two random variables | probability mass function explained with dice example · Maximum of two random variables · Functions of random variables | PMF convolution & key distributions · Minimum & maximum of two random variables · Mutiple random variables : Visualizing functions of two random variables
- Week 37 lecturesExpected value of a random variable | examples & distributions · Properties of expected value · Simulation of expected value using python · Variance & standard deviation | definition properties & examples · Covariance & its properties · Correlation coefficient · Bounds in probabilities using mean & variance | markov & chebyshev inequalities
- Week 413 lecturesExpectation, variance and Covariance: Expected value of random variable · Introduction to continuous random variables with examples · Cumulative distribution function | definition properties & examples · Approximating discrete CDF with a continuous function · General random variables & continuous random variables · Probability density function | definition properties & examples · Common distributions of continuous random variables | uniform exponential & normal statistics · Expectation, variance and Covariance: Bounds in probabilities using mean and variance · Illustration of continuous random variable in colab · Continuous random variable - Uniform distribution · Continuous random variable - Uniform distribution: applications · Continuous random variable - Non uniform and triangular distribution · Continuous random variable - Exponential distribution
- Week 54 lecturesFunctions of continuous random variables | PDF & CDF methods with examples · Expectations of continuous random variables | mean variance & inequalities · Motivation for multiple discrete/continuous random variables · Joint distribution of discrete & continuous random variables
- Week 67 lecturesJoint continuous random variables · Marginal densities of multiple continuous random variables · Multiple discrete/continuous random variable-Joint distributions:discrete and continuous · Independence of multiple continuous random variables · Conditional density of multiple continuous random variables · From data to distribution · Summarizing discrete/continuous random variable data & data in python colab
- Week 76 lecturesStatistics from samples and limit theorems: statistics from i.i.d. samples · Statistics from samples and limit theorems: empirical distribution and... · Statistics from samples and limit theorems: Illustrations with data · Statistics from samples & limit theorems: sum of independent random variables I · Statistics from samples and limit theorems: concentration phenomenon · Statistics from samples and limit theorems: Central Limit Theorem
- Week 84 lecturesStatistics from samples & limit theorems: moment generating functions (MGF) · Statistics from samples & limit theorems: central limit theorem (CLT) · Statistics from samples & limit theorems: distribution, properties & connections · Statistics from samples & limit theorems: descriptive statistics of normal samples
- Week 910 lecturesParameter estimation: statistical problems in real life · Parameter estimation: introduction to parameter estimation · Parameter estimation: error in estimation · Bias, variance & risk of an estimator · Estimator design approach: method of moments · Parameter estimation: estimator design approach: maximum likelihood · Parameter estimation: evaluation of ML estimators · Parameter estimation: finding MME & ML estimators · Parameter estimation: properties of estimators · Parameter estimation: confidence intervals
- Week 105 lecturesBayesian estimation - bayesian estimation · Bayesian estimation: choice of prior & examples · Bayesian estimation: problems: finding estimators · Bayesian estimation: problems: fitting distributions · Bayesian estimation: problems: model estimation
- Week 118 lecturesHypothesis testing: introduction to hypothesis testing · Hypothesis testing: size & power of a test (problems) · Hypothesis testing: types of hypothesis testing · Hypothesis testing: standard testing methods: z-test · Hypothesis testing: p-value · Hypothesis testing: z-test problems · Hypothesis testing: more problems on z-test · 4: Hypothesis testing: answering questions using data
- Week 1210 lecturesHypothesis testing: t-test, chi-squared test, two-sample z/f test · Hypothesis testing: t-test for mean (variance unknown) & · Hypothesis testing: two samples from normal distribution · Hypothesis testing: two samples test · Hypothesis testing: problems on t-test, chi-squared test & two-sample z/f test · Hypothesis testing: more problems on t-test, chi-squared test & two-sample z/f test · Hypothesis testing: problems on two-sample test · Hypothesis testing: likelihood ratio tests · Hypothesis testing: goodness of fit for discrete distributions · Hypothesis testing: goodness of fit for continuous distributions and...
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