Probability 

Content

Objective

-The aim of this course is to introduce the fundamental concepts of probability theory and basic statistical methods used in data science and applied mathematics. Students will learn how to model uncertainty, analyze random phenomena, and interpret probabilistic models.

Course Content

This course covers the basic concepts of probability, conditional probability, and independence. Random variables and probability distributions will be introduced through both discrete and continuous models. Discrete distributions such as Bernoulli, Binomial, and Poisson distributions, as well as continuous distributions including Uniform, Normal, and Exponential distributions, will be studied. Joint distributions and related concepts will also be discussed. In addition, expectation, variance, and covariance will be introduced together with important theoretical result such as the Central Limit Theorem.-

Course Learning Outcomes

Upon successful completion of this course, students will be able to:

Explain the fundamental concepts of probability theory.
Compute conditional probabilities and analyze independence between events.
Define and work with random variables and probability distributions.
Analyze discrete and continuous probability distributions.
Compute expectation, variance, and covariance of random variables.
Interpret and use joint probability distributions.
Explain the Central Limit Theorem.
Apply probabilistic methods to simple problems arising in data science and applied mathematics.

Weekly Contents