Probability and Statistics

Included:

• Elements of combinatorics.
• Probability of random events.
• Independence of random events.
• Random vectors: marginal and conditional distributions.
• Functions of random variables.
• Numerical properties of random variables: mathematical expectation, variance of a random variable, correlation coefficient between two random variables.
• Central border theorem.
• Elements of statistics: population and sample, parameters and statistics.
• Basic data processing and descriptive statistics.
• Sample statistics distributions: normal, t-distribution, Chi-square and F-distribution.
• Evaluation of landmark parameters: method of moments, method of maximum suitability, confidence intervals.
• Parameter tests.
• Nonparametric tests.
• Linear regression, estimation by the least squares method.m events.
• Properties of probabilities.
• Discrete probability space.
• Conditional probability.