Probability and Statistics

Program overview

Part I

• Axioms, conditional probability, Bayes rule, combinatorial analysis.
• Random variables: functions of distribution, mass and density, expectation and variance.
• Discrete and continuous probability laws.
• Reliability.
• Random vectors: correlation, multinormal distribution, central limit theorem
• Stochastic processes: Markov chains, Poisson process, Brownian motion.
• Descriptive statistics: diagrams, calculation of characteristics.
• Sampling distributions: estimate, mean squared error, confidence intervals. - Hypothesis tests: parametric tests and fit test. Simple linear regression.

Part II

• Discrete time and continuous time Markov chains.
• Birth and death process.
• Brownian movement. -Dissemination process. -Poisson process.
• Non-homogeneous Poisson processes and other generalizations.
• Renewal process.
• Queues with one and with multiple servers.