UAIC
Computer Science Department

Probability Theory and Statistics

Olariu Emanuel Florentin

Spring/Summer 2018-2019


Summary

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


Administrative

Lectures: weekly in C403 (in english) and C112/C2 (in romanian)

Lecturer:  Olariu E. Florentin- C212, C building, phone: 0232 20 15 46, olariu 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 - 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 and must retake all the tests in the arrears session.

  • Laboratories. The score comes partially from the presence and activity in 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 and must retake all the homeworks in the arrears session.
  • For other details see the first lecture.

Prerequisites: Knowledge of basic analysis and algebra.


Seminars/laboratories situations:

  • English groups
  • A1-4 groups
  • A6-7 groups
  • B3-4, A5 groups
  • B5-6 groups

  • 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.
    • Computer simulation: Monte Carlo methods.
    • Estimating lengths, areas, and volumes. Monte Carlo integration. Estimating probabilities.

     


    Lectures: