Probabilities and Statistics

Course Code: Ν2-2020
Weekly Duty: 4 (2Th + 2E)
ECTS: 5
Typical Semester: 2nd
Course Category: General Infrastructure Course
Prerequisites:  

Course Content
  1. Descriptive Statistics
    • Introduction, Population- Sample
    • Measures of position and scale
    • Proportion- standard error
    • Research studies- Graphs – Data Analysis
    • Confidence Intervals (tests) – A first approach
  2. Random Variables – Distributions
    • Random Variables (rv) – Probability density function
    • Commutative density function
    • Discrete rv : Binomial, Poisson
    • Continues rv : Exponential, Uniform
    • Normal distribution (standard, CLT)
    • Calculating E(X), V(X), etc
    • Defining tn, Χ2, Fm,n distributions
    • Propagation of the errors
    • Two-dimension Normal distribution
  3. Maximum Likelihood Estimators (MLE)
    • Definition of Maximum Likelihood Function
    • Examples of MLE
    • Confidence Intervals (tests)
    • Explain 6σ confidence intervals
    • Reliability – first approach
    • Fisher’s Information – Gramer-Rao theorem
  4. Regression Analysis (and LSM)
    • Simple Linear Regression
    • Normal Equations
    • Polynomial and Exponential Regression
    • The General Linear Model (GLM)
    • ANOVA
    • Cosinor models
  5. Entropy
    • Definition – Examples
    • Joined Entropy
    • Application to 2-dimension Normal distribution
    • Conditional Entropy
    • Application to Physics etc
  6. Stochastic Processes
    • Definitions and new approach development
    • Markov, Poisson,Wiener etc
    • Spectral Power (Spectral density)
    • Linear Systems
    • Introduction to Reliability (components in parallel, series, switch on/off etc)
    • The stochastic process development of Reliability
    • The Reliability in Engineering – flow charts – decisions
    • Calculating probabilities for problematic components
  7. Theoretical background to Probablity
    • Characteristic functions (Fourier transformations)
    • Moment Generating function (Laplace transformations)
    • Operators : ex. Expected value
    • Convolution Theorem – application to Statistics
    • Applications
  8. Sampling Theory
    • Simple random sampling
    • Stratified sampling
    • Other sampling techniques
    • The cost influence on sampling
    • Sequential sampling
    • The Wald Theorem
    • The Sequential procedure as a stochastic process

Literature
  1. Χ. Π. Κίτσος (2007) Τεχνολογικά Μαθηματικά και Στατιστική τόμος ΙΙ. Εκδ. Νεων Τεχνολογιών.
  2. Χ. Π. Κίτσος (2000) Υπολογιστική Στατιστική. Εκδ Νεων Τεχνολογιών
  3. Karlin, S. and Taylor, H. (1975). A first course in StochasticProcesses. Wiley
  4. Gray, R. and Davinson, L. (2004). An Introduxtion to Statistical Signal Processing.Campridge.

Internationalisation I18n