Probability and Statistics

Prerequisite Knowledge

It is recommended for the students to have the basic background in Mathematical Analysis I and II.

Course Units

#	Title	Description	Hours
1	Introduction	Random experiments, Historical review, Set theory.	2
2	Introduction to Probability	Sample space, Events, Definitions of probability, Axioms of probability, Conditional probability, Independence, Elements of combinatorics, Exercises.	10
3	Univariate Random Variables	Discrete and continuous random variables, Distribution function, Probability mass function, Probability density function, Exersices.	4
4	Moments of Random Variables	Expectation, Variance, Standard deviation, Moments, Exercises.	4
5	Specific Discrete Distributions	Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson, Exercises.	4
6	Specific Continuous Distributions	Uniform, Normal, Exponential, Gamma, Weibull, X2, Exercises.	4
7	Functions of Random Variables	Discrete case, Continuous case, Distribution of the sum of random variables, Distribution of the maximum and minimum, Exercises.	4
8	Central Limit Theorem	Approximate distribution of independent and identically distributed random variables, Approximate distribution of the sample mean of independent and identically distributed random variables, Approximation of Binomial by the Normal distribution, Exercises.	4
9	Introduction to Statistics	Introduction to the problem. Random sample and sampling distributions. Elements of descriptive statistics.	2
10	Point Estimation	Unbiasedness, Method of moments, Method of maximum likelihood, Exercises.	8
11	Confidence Intervals	Introductory notions and definitions, Interpretation of a confidence interval, Applications based on the normal distribution, Approximate confidence intervals, Connection to hypothesis testing, Exercises.	6

Learning Objectives

The module Probability - Statistics delivers an introduction in the modeling and analysis of stochastic systems. Its aim is to familiarize the students with the notions of random variables, distributions and parameters of them, as well as to develop skills in stochastic quantitative calculations. Additionally, methods of estimating unknown quantities are introduced, using Statistical techniques, with the help of a random sample.

Teaching Methods

Teaching methods	Lectures in class. Implementations using examples, exercises and case studies.
Teaching media	Blackboard

Student Assessment

• Final written exam: 70%
• Mid-term exam: 30%

Textbooks - Bibliography

1. Kokolakis, G. & Spiliotis, I (2010). Probability Theory and Statistics with Applications. Symeon. Athens (In Greek).
2. Vonta, I. & Karagrigoriou, A. (2017). Applied Statistical Analysis and Elements of Probability. Paraskinio. Athens (In Greek).
3. Fouskakis, D. (2013). Data Analysis using R. Tsotras. Athens (In Greek).
4. Kokolakis, G. & Fouskakis, D. (2009). Statistical Theory and Applications. Symeon. Athens (In Greek).
5. Bertsekas, D. & Tsitsiklis, G. (2013). Introduction to Probability and Elements of Statistics. Tziolas. Athens (In Greek).
6. Roussas, G. (2011). Introduction to Probability Theory. Ziti. Athens.
7. Hoel, P.G., Port, S.C. & Stone, C.J. (2009). Introduction To Probability Theory. University of Crete, Heraklion (In Greek).
8. Ross, S. (2011). Basic elements of Probability Theory. Klidarithmos. Athens (In Greek).
9. Spiegel, M.R. (Translation Persidis, S.) (1977). Probability and Statistics. Espi. Αthens (In Greek).
10. Class notes and Exercises in the following url : http://www.math.ntua.gr/~fouskakis/civil-eng.html.

Lecture Time - Place:

• Tuesday, 08:45 – 10:30,
  Rooms:
  • Ζ. Κτ. 1 Πολ., Αιθ. 1
• Thursday, 12:45 – 14:30,
  Rooms:
  • Αμφ. 1/2