Fundamentals of probability

Probability and events

1. Probability and probability measures

2. Zero-probability events

3. Conditional probability

4. Bayes' rule

5. Independent events

6. Multiple choice tests: Test 1

Random variables and random vectors

1. Random variables and univariate probability distributions

2. Random vectors and multivariate probability distributions

3. Expected value

4. Expected value and the Lebesgue integral

5. Properties of the expected value

6. Variance

7. Covariance

8. Linear correlation coefficient

9. Covariance matrix

10. Indicator functions

11. Multiple choice tests: Test 2, Test 3

Conditional probabilities, conditional distributions and independence

1. Conditional probability as a random variable

2. Conditional probability distributions

3. Conditional expectation

4. Independent random variables