Probability Ι (7,5 ECTS)

Course Code: 
6001
Semester: 
1st

Discrete probability spaces, elementary combinational analysis. Probabilities properties. Conditional Probabilities, Law of Total Probability. Bayes theorem. Discrete random variables, Joint distribution of random variables. Independence. Mean value, Variance, Covariance, correlation coefficient. Cauchy-Schwarz inequality, Markov and Chebyshev inequalities. Uniform, binomial, geometric and hypergeometric distributions, Poisson distribution. Uniform, binomial, geometric and hypergeometric distributions, Poisson distribution. Conditional mean value. The Weak Law of Large Numbers. Probability generating function. Multinomial and Multivariate hypergeometric distribution.

Continuous distributions. Distribution function and probability density function. Mean, variance. Uniform, exponential and normal distribution. Gamma and Beta distributions. Moment generating functions. Joint continuous variable distribution. independency. Random variables simulation using the method of inverse transformation.

Recommended reading

  • Κούτρας Μ., Εισαγωγή στη Θεωρία Πιθανοτήτων και Εφαρμογές, Εκδόσεις ΤΣΟΤΡΑΣ ΑΝ ΑΘΑΝΑΣΙΟΣ, 2016.
  • Feller, W. (1968). An Introduction to Probability Theory and its Applications. Wiley, N.Y.
  • Hoel P., Port S., Stone C., Εισαγωγή στη Θεωρία Πιθανοτήτων,  ITE Παν/κές Εκδόσεις Κρήτης, 2009.
  • Hogg, R. and Graig, A. (1970). Introduction to Mathematical Statistics, Third Ed., The Macmillan Co., New York.
  • Hogg,R.V. and Tanis,E.A. (2000). Probability and Statistical Inference. Prentice Hall.
  • Mendenhall, W., Beavec R.J. & Beaver, B.M. (1999): Introduction to Probability & Statistics (10th edition), Duxbury Press.
  • Mood, A., Graybill, F. and Boes, D. (1974). Introduction of the Theory of Statistics. McGraw-Hill.
  • Ross, S. (1976). A First Course in Probability. Collier, Macmillan, New York.
  • Ross, S. (1983). Introduction to Probability Models. 2nd Ed. Academic Press, New York.
  • Roussas, G.G. (2003). An introduction to Probability and Statistical Inference. Academic Press.
  • Ε.Ξεκαλάκη, Ι.Πανάρετος (1998) Πιθανότητες και Στοιχεία Στοχαστικών Ανελίξεων.

(old course title: Introduction to Probabilities)