Calendar

Week 1

Lecture

Basic concepts of probability and areas of formation.

Necessary foundations include: set theory and combinatorics.

Probability space, random variables, and Kolmogorov’s principles in the discrete case.

Syllabus PDF

Week 2

Lecture

Conditional Probabilities and Bayes’ Theorem.

Conditional Independence and Markov Chain Law, Statistical Independence.

Assignment 1

Week 3

Lecture

Repeated tests, Bernoulli trial, example solving, and review.

Probability space, random variable in continuous state.

Week 4

Lecture

Redefinition of random variables, distribution functions, and probability density functions.

Special random variables such as Gaussian, Poisson, etc.

Week 5

Lecture

Continuation of special random variables.

Statistics of a random variable: Mean, variance, etc.

Assignment 2

Week 6

Lecture

Conditional distributions.

Functions of random variables: Distribution and probability density functions, moments, and characteristic functions.

Week 7

Lecture

Joint distribution of random variables, bivariate distribution, marginal distribution, and…

Univariate functions of two random variables.

Practical Assignment

Week 8

Lecture

Two-dimensional functions of two random variables: Distribution function.

Central Limit Theorem.

Assignment 3

Week 9

Lecture

Week 10

Lecture

Assignment 4

Week 11

Lecture

Week 12

Lecture

Assignment 5

Week 13

Lecture

Week 14

Lecture

Assignment 6