- What is statistics and what is probability?
- Discrete probability spaces
- Examples of discrete probability spaces
- Countable and uncountable
- On infinite sums
- Basic rules of probability
- Inclusion-exclusion formula
- Bonferroni's inequalities
- Independence - a first look
- Conditional probability and independence
- Independence of three or more events
- Subtleties of conditional probability
- Discrete probability distributions
- General probability distributions
- Uncountable probability spaces - conceptual difficulties
- Examples of continuous distributions
- Simulation
- Joint distributions
- Change of variable formula
- Independence and conditioning of random variables
- Mean and Variance
- Makov's and Chebyshev's inequalities
- Weak law of large numbers
- Monte-Carlo integration
- Central limit theorem
- Poisson limit for rare events
- Entropy, Gibbs distribution
- Introduction
- Estimation problems
- Properties of estimates
- Confidence intervals
- Confidence interval for the mean
- Actual confidence by simulation
- Hypothesis testing - first examples
- Testing for the mean of a normal population
- Testing for the difference between means of two normal populations
- Testing for the mean in absence of normality
- Chi-squared test for goodness of fit
- Tests for independence
- Regression and Linear regression