Probability Theory and Statistics

Graphical and numerical summaries of data

Introduction to probability

Some elementary combinatorics to find probabilities

Conditional probability; Bayes' rule; stochastic (in)dependence

Random variables; probability mass function; density function; distribution function

Standard distributions: Binomial, Poisson, Geometric, Normal, Uniform, Exponential, Pareto

Expectation and variance; transformations; Jensen's inequality

Multivariate random variables; joint distributions; joint and marginal density functions; (in)dependence of random variables

Covariance and correlation

Chebychev's inequality; Law of Large numbers; Central Limit Theorem

Sampling theory and statistical models; mean, sample variance, histogram, empirical distribution function, boxplot

Theory of Estimators: Bias, Efficiency, Mean squared error

Linear Regression: univariate and multivariate, categorical variables, goodness of fit

Confidence intervals for Mean and Proportion; t-distribution

Testing theory: Type I/II Error, p-value, significance level, critical region, multiple testing, p-hacking

Hypothesis tests on mean(s), proportion(s), variance, regression parameters