UAIC
Computer Science Department

Probability Theory and Statistics

Olariu Emanuel Florentin

Spring/Summer 2019-2020


The score T2 (from statistics laboratories) will be composed from 20 points (the presence) + 40 points (the homeworks)

Arrears and enhancements: students can choose the Probability theory tests to take and the Statistics homeworks to present in order to increase their grades.

Probability theory tests on 18 of June:

  • halfyear B and E3, E4 groups on Google Classroom coordinated by prof. A. Zalinescu;

  • halfyear A and E1, E2 groups on Zoom coordinated by prof. E. F. Olariu.

The schedule for Probability theory tests is:

  • test 1: 8:00-8:15, the interval 8:15-8:20 is reserved to gather the results,

  • test 2: 8:25-8:40, the interval 8:40-8:45 is reserved to gather the results,

  • test 3: 8:50-9:05, the interval 9:05-9:10 is reserved to gather the results,

  • test 4: 9:15 si 9:30, the interval 9:30-9:35 is reserved to gather the results,

  • test 5: 9:40 si 9:55, the interval 9:55-10:00 is reserved to gather the results,

  • test 6: 10:05 si 10:20, the interval 10:20-10:25 is reserved to gather the results.


Statistics homeworks will be sent between 16 and 17 of June like follows:

  • halfyear B and E3, E4 groups to prof. A. Zalinescu at one of these two addresses: adrian.zalinescu@info.uaic.ro or adrian.zalinescu@gmail.com;

  • halfyear A and E1, E2 groups on to prof. E. F. Olariu at one of these two addresses: olariu@info.uaic.ro sau fe.olariu@gmail.com


Students from group X may choose an on-line meeting for taking the tests and an address from above to sent their homeworks.


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 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.


Final grades:

  • After the enhancements and arrears exam: halfyear A, E1, E2 and X group
  • Halfyears A, B, E1, E2, E3, E4 and X group
  • Seminars/laboratories final situations:

  • After the enhancements and arrears exam: halfyear A, E1, E2 and X group
  • Halfyears A, B, E1, E2, E3, E4 and X group

  • 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.
    • Randomized algorithms. Las Vegas and Monte Carlo algorithms.
    • Probabilistic method: satisfiabilty and graph theory applications.
    • 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.
    • Z-test for the means of two population with known variances.
    • F-test for the ratio of variances.
    • Linear correlation. The correlation coefficient and the standard deviation line.
    • Linear regression. Regression line.

     


    Probability Theory Lectures: