Probability & Statistics

This course provides a comprehensive exploration of probability and statistics, with a strong emphasis on practical applications and data analysis. The course is divided into two main parts:

In the first part of the course, students will focus on discrete probabilities and basic statistics. Key topics include:

• Descriptive statistics
• Probability theory and discrete distributions
• Conditional probability and Bayes theorem
• Random variables
• Markov chains and Poisson processes

In the second part of the course, students will focus on continuous probabilities and advanced statistics. Key topics include:

• Continuous random variables
• Linear regression and correlation
• Interval estimators and Monte Carlo estimators
• Information theory
• Hypothesis testing

Simulation and sampling methods implemented in Python/Pandas are integral to this course, providing hands-on experience and deeper insights into the concepts discussed.

The primary objective of this course is to equip students with a solid understanding of probability and statistics, enabling them to apply these concepts to real-world scenarios. 

By the end of the course, students will be able to:

• Comprehend and utilize discrete and continuous probability distributions.
• Apply conditional probability and Bayes' theorem in various contexts.
• Model stochastic processes using Markov chains and Poisson distributions.
• Conduct statistical analysis using correlation and covariance,
• Train and apply prediction techniques, such as linear regression.
• Fit probability distributions to data and estimate confidence intervals.
• Use information theory to measure information content and compress data.
• Perform hypothesis testing and make informed decisions based on statistical data.
• Utilize simulation and sampling methods for data analysis.

In presence

This course employs a blended approach to ensure a thorough understanding of probability and statistics.

• Theory lectures: Weekly sessions covering theoretical concepts and foundational knowledge.
• Exercises: Interactive weekly sessions for problem-solving and deeper engagement with simulation code.
• Projects: An individual project applying Markov chain for the creation of an autonomous agent playing tic-tac-toe, using Python/Pandas.
• Assessments: Midterm and final written exams, along with the project submission, to evaluate understanding and application of course material.

Active participation in all components is essential for success. Simulation and sampling methods are integral throughout the course, providing practical data generation and analysis experience. They are extensively used in the course project.

The course assessment consists of an optional midterm exam, a final exam, and a mandatory individual project. The midterm exam covers the first half of the course and contributes to 50% of the final grade. The final exam is split into two separate written exams, covering respectively the first and second part of the course. The first half of the final exam can be skipped by students who pass the midterm exam. The second half is mandatory for all students and contributes to the remaining 50% of the final grade. The individual project is graded as PASS/FAIL; getting a PASS is mandatory to pass the exam.