Contents: Probability, Set Operations; Properties of Probability; Finite Sample Spaces, Some Combinatorics; Multinomial Coefficients, Union of Events; Matching Problem, Conditional Probability; Independence of Events; Bayes\' Formula; Random Variables and Distributions; Cumulative Distribution Functions; Marginal Distributions; Conditional Distributions, Multivariate Distributions; Functions of Random Variables, Convolution; Functions of Random Variables: Sum, Product, Ratio, Maximum, Change of Variables; Linear Transformations of Random Vectors; Expectation, Chebyshev\'s Inequality; Properties of Expectation, Variance, Standard Deviation; Law of Large Numbers, Median; Covariance and Correlation, Cauchy-Schwartz Inequality; Poisson Distribution, Approximation of Binomial Distribution, Normal Distribution; Normal Distribution, Central Limit Theorem; Central Limit Theorem, Gamma Distribution, Beta Distribution; Estimation Theory, Bayes\' Estimators; Bayes\' Estimators; Maximum Likelihood Estimators; Chi-square Distribution, t-distribution, Confidence Intervals for Parameters of Normal Distribution; Confidence Intervals for Parameters of Normal Distribution; Hypotheses Testing, Bayes\' Decision Rules; Most Powerful Test for Two Simple Hypotheses; t-test; Two-sample t-test, Goodness-of-fit Tests, Pearson\'s Theorem; Simple Goodness-of-fit Test, Composite Hypotheses; Contingency Tables, Tests of Independence and Homogeneity; Kolmogorov-Smirnov Goodness-of-fit Test. |