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

a) construct appropriate probability spaces; 

b) compute probabilities by modeling sample spaces;

c) use basic standard distributions;

d) operate freely with independence, conditional probability, systems of random variables and their moment generating functions;

e) apply probability axioms and rules in probability: Bayes’ theorem, law of total probability, conditional expectation, law of large numbers, and central limit theorem; 

f) describe the main properties of probability distributions and random variables;

g)  construct discrete Markov chains and investigate their properties by using of limit theorems.