Course Program
DESCRIPTIVE STATISTICS
Basic notions: population, sample, statistical unit and statistical variable.
Classification of statistical variables.
Frequency distributions: absolute, relative, percentage, cumulative frequencies.
Joint distributions: marginal and conditional distributions.
Graphical representations: bar chart, pie chart, histogram, empirical distribution function.
Measures of central tendency: mode, median, and arithmetic mean.
Measures of variability: heterogeneity, dispersion, concentration.
Measures of form: asymmetry and kurtosis.
Statistical relationships between two variables: absolute independence, independence on average, correlation and relative measures.
PROBABILITY
Probability calculus: definition of experiment, event, probability, sample space.
Operations between events (negation, union, and intersection), basic axioms and derived theorems, elementary events and compound events, relationships between events (inclusion, incompatibility, and independence).
Bayes’ theorem.
STATISTICAL INFERENCE
Random variables: probability distribution, density function, and distribution function.
Distributions for discrete random variables (Discrete Uniform distribution, Bernoulli, Binomial) and continuous (Continuous Uniform, Normal).
Limit theorems: Law of Large Numbers, Central Limit Theorem.
Principles of statistical inference: random sample and sampling distribution.
Notable sampling distributions (mean, proportion, variance, difference between proportions, difference between means, ratio between variances), likelihood function.
Theory of estimation: estimators and estimation of a parameter, properties of estimators, methods for constructing estimators.
Point estimation and interval estimation.
Random intervals and confidence intervals (for mean, proportion, variance, difference between proportions, difference between means, ratio between variances).
Hypothesis testing: characteristics and logic of a statistical test, Neyman-Pearson lemma, operational procedure for a hypothesis test, tests on: mean, proportion, variance, difference between proportions, difference between means, ratio between variances.
Simple linear regression model: assumptions underlying the classical model, estimation of the model’s parameters and properties of the estimators, Gauss-Markov theorem, linear determination index, inference on the model’s parameters and on the linear determination coefficient.
