The statistical survey. Classification of variables. Frequency distribution of a descriptive variable. Graphic representations. Cumulative function.
Density for class distributions. Data numerical description. Central tendency measures: mode, mean and median. Variability measures: variation range and interquartile coefficient, variance and mean square deviation, variation coefficient
Asymmetry measures. Relationships between variables. Linear Relationships: Regression Model.
Random Experiment. Sample space. Sets of events. Properties of sets of events. Conditional Events. Axiomatic definition of probability according to Kolmogorov. Elementary laws of probability. Operative definitions of probability: combinatorial, frequentist and subjective. Conditional probability. Independent Events. Total probability theorem. The Bayes Theorem. Random variables and distribution functions: discrete and continuous. Cumulative function. Expectation value. Central tendency and dispersion around the mean. Mode, mean and median of a random variable. Variance and standard deviation. Chebychev's inequality and the meaning of standard deviation. Independence between random variables. Discrete random variables: Uniform, Bernoulli, Binomial, Poisson. Probability density function. Continuous random variables: Normal, t-Student, Chi-Square, Fisher. Central limit theorem.
The inferential problem. The probabilistic sampling. Sample statistics and parameter estimators. Correctness, efficiency, consistency of an estimator. Sample mean and sample variance. Point Estimate. Confidence interval. Decisions under uncertainty: hypothesis tests. Significance level and critical values. Type I and Type II errors.
Estimation of the regression curve of a bivariate population: The least squares method and the method of maximum likelihood. Linear regression. Statistical significance of the regression line. Intercept and gradient confidence intervals.