Introduction to Statistics. Random Variable, Mean, Variance, Standard Deviation and Mathematical Expectation. Discrete Distributions: Bernoulli trials and Bernoulli distribution, geometric distribution, Poisson distribution.
Continuous Distributions: random variables of the continuous type, uniform distribution, exponential distribution, gamma distribution, chi-square distribution, normal distribution, t-distributions.
Estimation: biased and unbiased esimators, convidence intervals for means, convidence intervals for varinces, sample size, maximum error of the point estimate, Likelihood function, Maximum Likelihood Estimation (MLE), Asymptotic Distributions of Maximum Likelihood Estimators, Chebyshev’s Inequality.
Hypothesis: tests of statistical hypotheses, Type I error, Type II error, tests about proportions, null hypothesis, alternative hypothesis, significance level of the test, probability value, tail-end probability, standard error of the mean, tests about one mean and one variance, test of the equality of two independent normal distributions, best critical region, Neyman-Pearson Lemma, most powerful test, uniformly most powerful critical region, Likelihood Ratio tests, critical region for the likelihood ratio test.
Pseudo-Numbers: uniform pseudo_random variable generation, congruential generators, shift-register generators, Fibonacci generators, Combinations of Generators (Shuffling).
The Inverse Probability Method for Generating RandomVariables. The Logistic Distribution.
Instructor: Marek Kimmel
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