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Mathematics IV
Lectures
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Week 13
Week 14
Random events and their probabilities.
Conditioned probability.
Independent events. Random variables (basic types and distribution functions).
Functional characteristics of discrete and continuous random variables.
Numeric characteristics of discrete and continuous random variables.
Basic discrete distribution laws. Classical, binomial, hypergeometric, Poisson distribution laws, their properties and applications.
Basic continuous distribution laws. Uniform, exponential, and normal distribution
laws, their properties and applications.
Random vector (n =2), types of random vectors, their functional and numeric characteristics.
Sampling, sample characteristics, samples of normal distribution, their properties.
Parameter estimates (point and interval estimates of normal distribution parameters).
Testing of statistical hypotheses (types of tests, basic concepts).
Testing hypotheses on normal distributions and their parameters.
Basics of regression analysis, linear regression model, point estimates.
Interval estimates and hypothesis testing for a linear regression model.
Seminars
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Week 13
Week 14
Descriptive statistics (one-dimensional population).
Descriptive statistics (two-dimensional population). Basic combinatorial formulas.
Probability (calculating classical probability using its properties).
Conditioned probability. Independent events.
Functional and numerical characteristics of random variables. Part 1
Functional and numerical characteristics of random variables. Part 2
Discrete distribution laws (binomial, hypergeometric, Poisson), approximation.
Continuous distribution laws (uniform, normal), approximation, tables.
Discrete random vector (n = 2), functional and numeric characteristics.
Point and interval estimates of normal distribution parameters.
Testing hypotheses on normal distribution parameters. Part 1.
Testing hypotheses on normal distribution parameters. Part 2.
Non-parametric tests.
Linear regression (straight line), estimates, tests and graph.