**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, bivariate (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, Matlab simulations of 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)

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, bivariate (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, Matlab simulations of 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)