Probability terms I., continuous variables. Probability terms II., discrete variables. Sampling distributions I., gamma distribution, beta distribution, Student?s t-distribution, F-distribution. Sampling distribution II., division two random variables, Central limit theorem. Relations among sample distributions. Some inequalities for binomial random variable, approximations of Poisson distribution, relations Poisson, binomial and F-distributions. Calculation algorithms for binomial, geometrical and Poisson distributions. Parameter estimations, average, sample variance, unbiased estimation, unbiased sample variance, bias of sample standard deviation, distributions of average and sample variance ? large sample, small sample. Parameter estimation, some use of order statistics. Order statistics, distribution of i-th order statistic, minimum and maximum distribution, symmetrical distribution, quantiles, sample median, parameters of uniform distribution estimation, Shifted exponential distribution. Parameter estimation, consistency, method of moments, maximum likelihood, MLE estimation for normal, exponential and uniform, sufficient statistic. Interval estimation. Parameter interval estimation, idea, vague of reliability interval, reliability interval symmetrical in probability, symmetrical in location, intuitive method for reliability interval construction. Tests of hypotheses. Simple hypotheses, simple alternative, type I. and II errors, its influence, rejection region, test power, most powerful and uniformly powerful test, Neyman-Pearson lemma, parameter tests, power function, exponential family testing, likelihood ratio tests. Tests of hypotheses, sequential tests, Wald?s tests, sequential tests about parameters, random count sums distribution, Wald?s tests properties in contrary classical tests. n-dimensional distribution, estimation, test and dependencyy models, two-dimensional normal distribution, detailed analysis, correlation, sample correlation, Fisher transformation, correlation interval estimation, independence (non-correlation) hypothesis. Non-parametrical tests, categorical variables distribution, goodness-of-fit test, modification, homogeneity test.
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