Probability and Statistics Overview

Basic Descriptive statistics and exploratory analysis

Defining data and variables

Exploring a single variable

Measures of center

Measures of spread

Examining relationships between two variables

• role-type
• side by side box plots
• 2-way tables
• scatter plots
• linear regression
• correlation

Sampling and study design

Basic Probability

Random processes, outcomes, events

(In)dependent events, Conditional probability and Baye's theorem

Counting methods

Measure theory

Random Variables and Distributions

Discrete and Continuous random variables

Probability density functions (PDFs) and Cumulative Distribution Functions (CDFs)

Important discrete random variables

Important continuous random variables

Bivariate distributions

Marginal distributions

Independent random variables

Conditional distributions

Multivariate distributions and IID Samples

Some important multivariate distributions

Transformation of random variables

Transformations of several random variables

Expectation

Inequalities

Convergence of Random Variables

Statistical inference