UAIC
Computer Science Department

Probability Theory and Statistics

ro en

Olariu Emanuel Florentin

Zalinescu Adrian

Spring/Summer 2026

Summary

This course aims to introduce basic topics in Discrete Probability Theory and Descriptive and Inferential Statistics.

Prerequisites: Knowledge of basic analysis and algebra.

Course information sheet: (ro) - (ai) - (en)

Administrative

Lecturers:

  Olariu E. Florentin - C212, C building, phone: 0232 20 15 46, emanuel dot olariu at info dot uaic ro

  Zalinescu Adrian - C307, C building, adrian dot zalinescu at info dot uaic dot ro

Office Hours: weekly, better by e-mail appointment.

Grading:

  • Seminars. The score comes from six small tests one on each seminar (15 minutes) - this score must be at least 30 (from a maximum of 6x10 = 60) points. Those who fail to receive at least 30 points cannot pass the course.
  • Laboratories. The score comes from the exercises solved in the class (20 points), from homeworks (20 points, deadline in the 13th week), and from a test given in the final week (20 points). This score must be at least 30 (from a maximum of 20 + 20 + 20 = 60) points. Those who fail to receive at least 30 points cannot pass the course.
  • For other details see the first lecture (ro) - (en) .
  • There is no arrears and enhancements session exam.
    Rules for uploading the homeworks:
  • connect with VPN SFTP to hostname s-submit.info.local (OpenVPN is recommended);
  • use the your credentials username/password @info.uaic.ro;
  • each student has a homeDirectory /some/storage// in which can upload its homeworks;
  • you can delete and/or upload the homeworks until 21 of May.
The statistics test from the last week is a written test (and will last for 20 minutes); you can use only the calculator from your phone. (The test will not contain exercises about the F test.)

Scores: seminars/laboratories

Final grades.

Bibliography:

  • Bertsekas, D. P., J. N. Tsitsiklis, Introduction to Probability, Athena Scientific, Belmont, Massachusetts, 2002.
  • Gordon, H., Discrete Probability, Springer Verlag, 2010.
  • Lipschutz, S., Theory and Problems of Probability, Schaum's Outline Series, McGraw Hill, 1965.
  • Ross, S. M., A First Course in Probability, Prentice Hall, 5th edition, 1998.
  • Stone, C. J., A Course in Probability and Statistics, Duxbury Press, 1996.
  • Freedman, D., R. Pisani, R. Purves, Statistics, W. W. Norton & Company, 4th edition, 2007.
  • Johnson, R., P. Kuby, Elementary Statistics, Brooks/Cole, Cengage Learning, 11th edition, 2012.
  • Shao, J., Mathematical Statistics, Springer Verlag, 1998.
  • Spiegel, M. R., L. J. Stephens, Theory and Problems of Statistics, McGraw Hill, 3rd edition, 1999.

List of Topics (weekly updated):

  • Introduction. Random experience.
  • Random (elementary) events, probability function.
  • Conditional probability, independent random events, conditional independence.
  • Total probability formula, Bayes formula.
  • Conditional version of the total probability formula. Multiplication formula. Probabilistic schemata: hypergeometric, Poisson, binomial, geometric.
  • Distribution of a discrete random variable.
  • Expectation and variance of a discrete random variable.
  • Remarkable discrete distributions: uniform, Bernoulli, binomial, geometric, Poisson.
  • Other remarkable discrete distributions: negative binomial, hypergeometric, Zipf.
  • Joint probability distribution.
  • Covariance and independence of random variables.
  • Markov's and Chebyshev's inequalities.
  • Chernoff's and Hoeffding's inequalities.
  • Continuous random variables. Distribution and density functions. Remarkable continuous distributions.
  • Fundamental laws: Chebyshev's and the Law of Large Numbers (LLN).
  • Fundamental laws: Central Limit Theorem (CLT). Approximation of the binomial distribution using the normal distribution (de Moivre-Laplace theorem).
  • Computer simulation. Illustrations of LLN and CLT.
  • Computer simulation: Monte Carlo methods.
  • Estimating lengths, areas, and volumes. Monte Carlo integration. Estimating probabilities.
  • Randomized algorithms. Las Vegas and Monte Carlo algorithms.
  • Probabilistic method: satisfiabilty problems applications.
  • Vocabulary of statistics. Descriptive statistics, variable, graphical representations.
  • Central tendency: mean, median, mode. Quartiles.
  • Variability measures: variance, standard deviation, interquartile range. Outliers.
  • Inferential statistics. Point and interval estimation - confidence intervals.
  • Statistical hypotheses testing. Errors, significance level and, the power of the test.
  • Proportions test. One- and two-tailed tests.
  • Z-test for the mean of a population with known variance.
  • T-test for the mean of a population with unknown variance.
  • Chi-square test for googdness-of-fit.
  • Chi-square test for statistical independence.
  • F-test for the ratio of variances.
  • Linear correlation. The correlation coefficient and the standard deviation line.
  • Linear regression. Regression line.

 

Discrete Probability Theory Lectures: