• Definition of terms: experiment, event, probability of an event,
random variable.
• Axiomatic, classical and statistical definition of probability.
• Theorems on probability calculus.
• Probability density and probability distribution functions:
definition, properties.
• Distributions: normal, binomial, Poisson, Pearson’s, Fischer’s.
• Function of a random variable.
• Characteristics of a random vector. Multinomial and multivariate
normal distribution.
• Population and sample. Generation of random numbers.
• Quantile characteristics.
• Theorems on one sample and two samples from a normal distribution.
• Confidence intervals: derivation, basic formulas.
• Testing of Hypothesis: general procedure, errors in testing.
• Tests: Pearson, Kolmogorov-Smirnov, Shapiro-Wilk, sign test of
independence, Kruscal-Wallis, Wilcoxon.
• Simple linear regression, model analysis.
• Assumptions of linear regression and their verification.
• Multiple linear and nonlinear regression.
• Analysis of variance (ANOVA).
• Analysis of correlation.
• Contingency tables, qualitative variables in regression analysis.
random variable.
• Axiomatic, classical and statistical definition of probability.
• Theorems on probability calculus.
• Probability density and probability distribution functions:
definition, properties.
• Distributions: normal, binomial, Poisson, Pearson’s, Fischer’s.
• Function of a random variable.
• Characteristics of a random vector. Multinomial and multivariate
normal distribution.
• Population and sample. Generation of random numbers.
• Quantile characteristics.
• Theorems on one sample and two samples from a normal distribution.
• Confidence intervals: derivation, basic formulas.
• Testing of Hypothesis: general procedure, errors in testing.
• Tests: Pearson, Kolmogorov-Smirnov, Shapiro-Wilk, sign test of
independence, Kruscal-Wallis, Wilcoxon.
• Simple linear regression, model analysis.
• Assumptions of linear regression and their verification.
• Multiple linear and nonlinear regression.
• Analysis of variance (ANOVA).
• Analysis of correlation.
• Contingency tables, qualitative variables in regression analysis.