**Lecture Schedule**

8/22 Introduction, prob vs stat, the reproducibility crisis, what is randomness?, simulation of coin flips illustrating law of large numbers,

Kolmogorov's Axioms of Probability and derivation of fundamental properties of probability

8/24 Properties of probability, independence, Birthday Problem, conditional probability

8/29 Bayes' theorem, application to screening of rare diseases and Span filtering, prior and posterior ideas of Baysian inference, random variables and their CDF

8/31 Examples of discrete random variables

9/5 More examples of discrete random variables: negative binomial, Poisson approximation of binomial, power law, continuous random variables: pdf and cmd, general properties, examples: uniform, exponential (and memoryless property), power law

9/7 Poisson process and waiting time to first event is an exponential random variables, normal random variables, lognormal random variables, skip for now other random variables, bi-variate (joint) distributions for discrete random variables, marginal mass function, independence of random variables

9/12 Class cancelled (Hurricane Irma)

9/14

9/19 Expected value

9/21 Exam 1

9/26 Variance and covariance

9/28 Correlation, variance-covariance matrix, simple random walk, Matlab motivations of LLN and CLT, Markov's inequality

10/3 Chebyshev's inequality, proof of Weak LLN, modes of convergence, statement of Strong LLN, moment generating functions

10/5 Properties of moment generating functions, statement of CLT, speed of convergence

10/12 Applications of moment generating functions, Levi continuity theorem, proof of CLT, applications of CLT, introduction to statistical inference (learning)

10/17 Examples of point estimation problems, properties of point estimators

10/19 Loose ends: applications of power-law distributions, when can one safely apply normal approximation, Slutsky's theorem and application to CLT with sample variance replacing population variance, tank problem with four estimators for N, variance of these estimators, confidence intervals (what they are, and what they are not)

10/24: Constructing confidence intervals using Chebyshev inequality and Hoeffding's inequality, application to estimating percentage of GT students infected with Norovirus last week, confidence intervals for asymptotically normal estimators, empirical distribution function

10/26 Properties of the empirical distribution function, DKW estimate and confidence intervals for the empirical distribution function, plug-in estimators

10/31 Estimating the difference between two means, examining the link between cholesterol and heart disease, confidence intervals for plug-in estimators, examining the link between cholesterol and heart disease, estimating variance of quotient of RVs, Bootstrap approach to estimating standard error

11/02 Exam 2

11/07 Bootstrap confidence intervals (3 methods), Method of Moments estimator and properties

11/09 Maximal Likelihood estimator and properties, Fisher information function, Cramer-Rao inequality

11/14 Properties of estimators

11/16 Hypothesis testing

11/21 Poofs of properties of MLE, hypothesis testing

11/23 Thanksgiving break

11/28 Hypothesis testing, Neyman-Pearson test, Wald tests

11/30 p-values, intro to Bayesian statistics

12/01 Intro to Bayesian statistics

Kolmogorov's Axioms of Probability and derivation of fundamental properties of probability

8/24 Properties of probability, independence, Birthday Problem, conditional probability

8/29 Bayes' theorem, application to screening of rare diseases and Span filtering, prior and posterior ideas of Baysian inference, random variables and their CDF

8/31 Examples of discrete random variables

9/5 More examples of discrete random variables: negative binomial, Poisson approximation of binomial, power law, continuous random variables: pdf and cmd, general properties, examples: uniform, exponential (and memoryless property), power law

9/7 Poisson process and waiting time to first event is an exponential random variables, normal random variables, lognormal random variables, skip for now other random variables, bi-variate (joint) distributions for discrete random variables, marginal mass function, independence of random variables

9/12 Class cancelled (Hurricane Irma)

9/14

9/19 Expected value

9/21 Exam 1

9/26 Variance and covariance

9/28 Correlation, variance-covariance matrix, simple random walk, Matlab motivations of LLN and CLT, Markov's inequality

10/3 Chebyshev's inequality, proof of Weak LLN, modes of convergence, statement of Strong LLN, moment generating functions

10/5 Properties of moment generating functions, statement of CLT, speed of convergence

10/12 Applications of moment generating functions, Levi continuity theorem, proof of CLT, applications of CLT, introduction to statistical inference (learning)

10/17 Examples of point estimation problems, properties of point estimators

10/19 Loose ends: applications of power-law distributions, when can one safely apply normal approximation, Slutsky's theorem and application to CLT with sample variance replacing population variance, tank problem with four estimators for N, variance of these estimators, confidence intervals (what they are, and what they are not)

10/24: Constructing confidence intervals using Chebyshev inequality and Hoeffding's inequality, application to estimating percentage of GT students infected with Norovirus last week, confidence intervals for asymptotically normal estimators, empirical distribution function

10/26 Properties of the empirical distribution function, DKW estimate and confidence intervals for the empirical distribution function, plug-in estimators

10/31 Estimating the difference between two means, examining the link between cholesterol and heart disease, confidence intervals for plug-in estimators, examining the link between cholesterol and heart disease, estimating variance of quotient of RVs, Bootstrap approach to estimating standard error

11/02 Exam 2

11/07 Bootstrap confidence intervals (3 methods), Method of Moments estimator and properties

11/09 Maximal Likelihood estimator and properties, Fisher information function, Cramer-Rao inequality

11/14 Properties of estimators

11/16 Hypothesis testing

11/21 Poofs of properties of MLE, hypothesis testing

11/23 Thanksgiving break

11/28 Hypothesis testing, Neyman-Pearson test, Wald tests

11/30 p-values, intro to Bayesian statistics

12/01 Intro to Bayesian statistics