Syllabus Information

5.3. Syllabus

Modules

Module 1: Exploratory data analysis in computer laboratory.

Module 2: Models of probability distribution.

Module 3: Sampling, estimation and hypothesis tests.

Module 4: Introduction to Optimization.

Module 1: Exploratory Data Analysis

Descriptive statistics

Basic concepts. Types of variables.

Data organization. Frequency table.

Graphic descriptions of a variable.

Numerical descriptions of a variable. Box-plot.

Bidimensional distributions. Bidimensional table.

Marginal and conditional distributions.

Measures of association. Regression and correlation.

Module 2: Models of probability distribution

Basic concepts. Sample space and events, algebra of events. Random and deterministic experiments.

Interpretations of probability.

Kolmogorov axiomatic definition.

Conditional probability. Independence of events.

Partition of a sample space, law of total probability and Bayes theorem.

Reliability of systems.

Random variables

Definition of random variable. Classification.

Discrete random variable, probability function, distribution function.

Continuous random variable, density function, distribution function.

Expectation of a random variable and of a function of a random variable.

Basic properties of expectation and variance

Moments of a random variable.

Other measures of central tendency and dispersion.

Chebyshev inequality.

Main discrete distributions: Bernoulli, binomial, Poisson, geometric, hypergeometric.

Main continuous distributions: uniform, exponential, normal.

Reproductivity of random variables.

Poisson process: relationship to exponential distribution.

Approximations between random variables.

Two-dimensional distributions. Calculation of expectations and variances of a linear combination of independent random variables.

Module 3: Sampling, estimation and hypothesis tests

Sampling and Estimation

Introduction. Basic concepts associated with sampling distributions in normal populations: chi-square, Student's t, F.

Distributions important statistical sampling: Central Limit Theorem and Fisher theorem.

Confidence interval estimation. Intervals for means, variances and proportions. Calculation of the minimum sample size.

Hypothesis tests: null and alternative hypothesis, level of significance.

Relationship between confidence intervals and hypothesis tests.

Calculating the p-value.

Hypothesis testing for means, variances and proportions.

Chi-square and tests of contingency tables.

Module 4: Introduction to Optimization

Optimization problems

Decision variables, objective function and constraints.

Linear programming problems: graphic resolution.

Contents of Practical classes in computer laboratory

• Uni-dimensional descriptive statistics.

• Instructions for implementation of the Statistical Report.

• Two-dimensional Descriptive Statistics. Regression and correlation.

• Probability distributions of discrete and continuous random variables.

• Test goodness of fit.

• Hypothesis testing for means, variances and proportions.

• Introduction to Optimization.