Information about the content of the module.

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