UAIC
Computer Science Department

Probability Theory and Statistics

ro en

Olariu Emanuel Florentin

Zalinescu Adrian

Spring/Summer 2025

Summary

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

Prerequisites: Knowledge of basic analysis and algebra.

Administrative

Lecturers:

  Olariu E. Florentin - C212, C building, phone: 0232 20 15 46, fe dot olariu at gmail dot com

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

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 partially from the exercises solved in the class (20 points) and partially from homeworks (40 points) whose end-terms are in the last week of the semester. This score must be at least 30 (from a maximum of 20+40=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 session exam.
  • Students who - for very good reasons - missed a test during the first six weeks could take the test (after contacting prof. Olariu by e-mail) on April 15:00, 9:00, C411.

Scores: seminars/laboratories

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, hypergeometric.
  • Joint probability distribution.
  • Covariance and independence of random variables.
  • Markov and Chebyshev inequalities.
  • Chernoff bounds. Hoeffding bounds.
  • Discrete Markov chains. Steady states, long term behavior. Random walks.
  • Vocabulary of statistics. Descriptive statistics, variable, graphical representations.
  • Central tendency: mean, median, mode. Quartiles.
  • Variability measures: variance, standard deviation, interquartile range. Outliers.
  • Continuous random variables. Density and distribution functions. Remarkable continuous distributions.
  • Fundamental laws: Law of Large Numbers (LLN) and Central Limit Theorem (CLT).
  • Computer simulation. Illustrations of LLN and CLT.

 

Probability Theory Lectures: