| Objectives | Students should be able to apply fundamental probabilistic models andmethods to solve problems related to the study of random phenomena; they should also be able to use the computer in order to apply statistical methods for decision making, based on experimental data.
Students should be able to recognise various types of random variables and to understand which variable can be used in given situations; they should also understand the basics of statisical reasoning, specifically to select and apply appropriate statistical tests for hypothesis testing. |
| General thematics | Descriptive Statistics: synthesis and presentation of experimental data (see seminar below).
Probability Theory: Events, operations over events. Conditional probability. The formula of Bayes. Random variables – repartition, operations, taxonomy. Discrete variables (bynomial, Poisson, geometric hipergeometric), continues variables (uniform, normal, exponential, gamma, Student, Chi Square,Weibull ,f). Moment generating functions. Vectors of random variables. Covariance. Corelation coefficient. Markov and Cebâşev inequalities. The strong law of large numbers. The Central limit theorem. Stochastic processes.
Inferential Statistics: Parameter estimation. Confidence intervals for poplation parameters. Hypothesis testing for means, proportions, dispersions. Inferences on multinomial experiments. Inferences over two populations. Dispersional analysis. |
| Seminary / Laboratory thematics | Students will practice, using EXCEL®, how to solve specific real world problems using notions from Probability Theory, as well as various methods of Descriptive Statistics for organising and presenting raw data (relative and cumulative frequencies; proportions; frequency distributions; graphical representation of random variables; measures of central tendency; measures of variation), as well as raw data processing for statistical analysis : confidence intervals for means, propotions, dispersions; significance tests for means, proportions, disperions, including non-normal populations; inferences for two populations; qualitative variables; the Chi-square test (independence, homogenity); dispersional analysis. |
| Teaching methods | exposition, problem-solving, case studies, exercise. |
| Bibliography |
- Johnson, R. : Elementary Statistics, PWS Publishers - Duxbury Press, Boston, 1991 (available in the Mathematics Library)
- Ciucu, Gh., Craiu, V.: Introducere în Teoria probabilităţilor şi Statistică matematică, Editura Didactică şi Pedagogică.
- Ciucu, Gh., Craiu, V., Săcuiu, I.: Probleme de Teoria probabilităţilor, Editura Tehnică.
- Blattner, P.: Microsoft® EXCEL, Editura Teora, 2002.
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A. I. Cuza University of Iaşi