Study Guide

Objective

In this course, the students learn the basic concepts of probabilities, random variables and random vectors. The students learn to compute discrete and continuous probabilities and expectation values such as variances and correlations. The students also learn to apply the probability calculus to practical problems. The students learn how to justify their claims using mathematical methods and to present their solutions orally as well as in written form.

Content

1. Basic Notions of Probability Theory: Probability and Expectation, Conditional Probability, Total probability and Independence Bayesian probability and Combinatorial analysis.
2. Random Variables: The Probability Mass and Density Functions, Important Discrete Random Variables, Important Continuous Random Variables and Expectation and Variance Moment Generating Function
3. Random Vectors: Discrete and Continuous Random Vectors, Covariance and Correlation, Multinormal Distribution and The Central Limit Theorem Transformations of Random Vectors

Assessment criteria, satisfactory (1)

Grading done by TUT

Assessment criteria, good (3)

Grading done by TUT

Assessment criteria, excellent (5)

Grading done by TUT