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Probability and Statistical Models


  • Basics of probability: Random experiment, sample space, axioms of probability, probability laws, Bayes’ theorem,
  • Random variables and probability distributions (classical discrete and continuous probability distributions) 
  • Moments of random variables,
  • Joint, marginal and conditional probability distributions 
  • Multivariate normal distribution, 
  • Moment-generating and characteristic functions, 
  • Convergence of sequence of random variables,
  • Law of large numbers and central limit theorem; 
  • Sampling distribution; 
  • Point and interval estimation: characteristics of good estimator, 
  • Methods of estimation: Least squares and Maximum Likelihood estimation, 
  • Testing of hypothesis concerning means, variances and proportions 
  • Non-parametric tests: One sample and two sample tests
  • Elements of generalized linear modeling. 
  •  Application in R. (as a Master’s course in Data Sciences, we recommend that the lecturer should consider examples and problems from real life (with some data sets) and applications in the software R).