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      Information about the content of the module. Lesson

      Course Overview:

          Probability theory forms the backbone of many techniques and algorithms in informatics. This course provides students with a solid foundation in probability theory and its applications in computer science. Through theoretical study and practical problems, students will develop the skills to model and analyze uncertain systems, make informed decisions in uncertainty, and apply probabilistic methods in various informatics domains.


      Subject content:

          By understanding probability theory, students can grasp the probabilistic nature of quantum systems, interpret measurement outcomes, and comprehend the principles underlying quantum mechanics and quantum computing. This foundational knowledge is essential for further exploration and advancement in quantum information science.


      Module content:

                                          

      1- Probability basics reminder:

           • Introduction to probability spaces, events, and sample spaces. 
           • Probability axioms and properties. 
           • Combinatory and counting techniques. 
           • Conditional probability and Bayes' theorem. 

           • Independence of events. 
      2- Random Variables: 

         • Discrete and continuous random variables. 
         • Probability mass functions and probability density functions. 
         • Cumulative distribution functions. 
         • Expected value, variance, and moments. 

      3- Probability Distributions: 

         • Bernoulli, binomial, and multinomial distributions. 
         • Poisson distribution. 
         • Gaussian (normal) distribution. 
         • Exponential and gamma distributions. 

      4- Probability distributions for combined random variables

         • Joint and marginal distributions of discrete random variables
         • Joint and marginal distributions of continuous random variables
         • Expectations of joint discrete and continuous distributions

      5- Conditional probabilities and independence
         • Conditional distribution of a discrete random variable and its properties
         • Conditional distribution of a discrete random variable and its properties
         • Conditional expectation and variance


      Evaluation:

      30%: Written-test
      70%: Exam


    • Glossary icon
      Key terms used in this module Glossary

      Here is a glossary of key terms used in this module; it covers some key terms and concepts in probability theory.


      - Probability: The measure of the likelihood that an event will occur.
      - Sample Space: The set of all possible outcomes of a random experiment.
      - Event: A subset of the sample space, representing a particular outcome or a collection of outcomes of interest.
      - Random Variable: A variable that can take on different values with certain probabilities, representing the outcomes of a random experiment.
      -  Expected Value (Mean): The average value of a random variable.
      -  Variance: A measure of  dispersion of a random variable




  • Chapter 1: Probability basics reminder

     In this chapter, we focus on the basic concepts of probability and  techniques for determining without direct enumeration the number of possible outcomes of a particular experiment or the number of elements in a specific set .



  • Chapter 2: Random Variables

  • Chapter 3: Probability distributions for combined random variables

       In this chapter, we focus on how we model the probability distribution of two (or more) random variables jointly, that are defined within the same sample space. We begin with the discrete case by seeking the joint probability mass function of two discrete random variables. Next, we will consider the continuous case.


  • Conditional probabilities and independence

      In this chapter, we define the probability distribution of one random variable given information about another random variable. This type of conditional distribution relies on the joint distribution of the two random variables introduced earlier. We begin with discrete random variables and then move on to the continuous case.