# MATH-F-105

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Contenu du cours

This is an introductory course to probability theory.

This is the tentative table of contents:

1.1. Sample space.

1.2. Events.

1.3. sigma-algebra.

1.4. Probabilities.

2.1. Laplace experiments.

2.2. Multinomial and hypergeometric distribution.

2.3. Discrete probability spaces.

2.4. From hypergeometric to binomial distribution.

2.5. Poisson distribution.

2.6. Geometric distribution.

3.1. Random variables.

3.2. The Borel $\sigma$-algebra.

3.3. Distribution functions.

3.4. Densities.

4.1. Expected value of a discrete random variable.

4.2. Examples.

4.3. Some results on convergence of series.

4.4. Properties.

4.5. The general case.

4.6. Variance and higher order moments.

4.7. Moment generating functions.

5.1. Conditional probability.

5.2. Total probability and Bayes' theorem.

5.3. Higher order models.

5.4. Independence of events.

5.5. Independence of random variables.

6.1. Random vectors and sequences.

6.2. Covariance and correlation.

7.1. Convergence in Lp and in probability.

7.2. The law of large numbers (LLN).

7.3. Applications.

8.1. Convergence in distribution.

8.2. The Central limit theorem.

8.3. Applications.

### • * Exercices (Solutions on Univ. virtuelle)*

Ex 1

Ex 2

Ex 3

Ex 4

Ex 5

Ex 6

Ex 7

Ex 8

Ex 9

Ex 10

Ex 11

### • * Sample Exam *

Exercises

Theory

Updated: May 16, 2017