Introduction:
Axiomatic definition of Probability, algebraic and analytic properties of probability measures.
Conditional Probability:
Total probability formula and Bayes’s formula, first-step analysis.
Discrete/Continuous Random Variables:
Probability mass/density functions, special distributions (Bernoulli, binomial, geometric, negative binomial, hypergeometric, Poisson, uniform, exponential, Gamma, normal, Cauchy) and their properties.
Cumulative Distribution Functions:
Moment generating and characteristic functions.
Multidimensional Distributions:
Joint, marginal, and conditional distributions; transformations of random vectors, special multidimensional distributions (polynomial, multivariate normal), and independence of random variables.
Indices of Distributions:
Mean, median, variance, covariance.
Modes of Convergence:
Convergence in probability, almost sure,
Lp, and distribution.
Probability Inequalities:
Markov, Chebyshev, Jensen, Paley-Zygmund, Chernoff.
Laws of Large Numbers and Monte Carlo Methods:
Applications of the Central Limit Theorem.
- Teacher: Μιχαήλ Λουλάκης
Τομέας: Μαθηματικών
ECTS : 5
Language : el