Шыныбеков Ә.Н., Ықтималдықтар теориясы және математикалық статистика элементтері, 2008

1.1. Sample space

1.2. Operations on random events

1.3. Elements of combinatorics

1.4. Probability of an event and its properties

1.4.1. Classical definition of event probability

1.4.2. Properties of probability

1.5. Geometric probability

1.6. Total probability of an event. Bayes' formula

1.6.1. Total probability formula

1.6.2. Bayes' formula

1.7. Repeated trials. Bernoulli formula and Poisson approximation formulas

1.8. Laplace approximation formulas

1.8.1. Local Laplace approximation formula

1.8.2. Integral Laplace approximation formula

1.8.3. Estimating the deviation of event frequency from probability

1.9. Random variables. Specification of discrete random variables

1.10. Types of discrete random-variable distributions

1.11. Numerical characteristics of discrete random variables

1.12. Continuous random variables

1.13. Two-dimensional random variables. Correlation coefficient

1.14. Chebyshev's inequality and the concept of the law of large numbers

2.1. Sample. Simple empirical distribution function. Histogram

2.2. Point estimation of unknown distribution parameters

2.3. Confidence-interval method for estimating an unknown parameter

2.4. Sample correlation coefficient. Linear regression

2.5. Statistical hypothesis testing

2.5.1. Statistical hypothesis. Null and alternative hypotheses. Simple and composite hypotheses

2.5.2. Type I and Type II errors

2.5.3. Statistical analysis of null-hypothesis testing. Observed value of the test statistic

2.5.4. Critical region. Acceptance region. Critical point

2.5.5. Finding critical regions

2.5.6. Comparing variances of two normally distributed populations

2.5.7. Comparing two normally distributed populations with known variances

2.5.8. Testing the hypothesis that a population is normally distributed

2.6. One-way analysis of variance

2.6.1. Concept of analysis of variance

2.6.2. One-way analysis of variance

2.6.3. Comparing several means using analysis of variance

2.6.4. Unequal numbers of trials at different levels

3. Independent-work assignments

3.1. Elements of combinatorics

3.2. Classical definition of probability

3.3. Geometric probability

3.4. Bernoulli formulas. Approximation formulas

3.5. Discrete random variable and its numerical characteristics

3.6. Continuous random variable and its numerical characteristics

3.7. Laplace approximation formulas

3.8. Point estimation of distribution parameters

3.9. Correlation analysis

3.10. One-way analysis of variance

3.11. Unequal numbers of trials at different levels

4. Test questions

Answers to test questions

Procedure for completing independent work

References

Appendices