## Probability Theory and Mathematical StatisticsProbability theory; Random events; Random variables; Parameters of the distribution of a Random variable; Characteristic functions; Some probability distributions; Limit theorems; Markov chains; Stochastic processes; Mathematical statistics; Sample moments and their functions; Order statistics; An outline of the theory of runs; Significance tests; The theory of estimation; Methods and schemes of sampling; An outline of analysis of variance; Theory of hypotheses testing; Elements of sequential analysis. |

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### Contents

RANDOM EVENTS | 3 |

RANDOM VARIABLES | 29 |

PARAMETERS OF THE DISTRIBUTION OF A RANDOM VARIABLE | 64 |

Copyright | |

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### Common terms and phrases

according alternative appearance applied arbitrary assume assumption asymptotically called characteristic function coefficient compute condition consider consists constant contains continuous type convergent defined Definition degrees of freedom denote density depend determined distribution function distribution function F(x drawing efficient elements equals equation estimate event example exists expected value expression fact finite follows formula give given hence holds hypothesis H independent independent random variables inequality integral interval limit Markov mean measure method moments normal distribution observed obtain parameter particular points Poisson population positive possible present probability probability function Problem proof Prove random event random variable reject relation respectively result satisfied sequence Show side simple samples statistic stochastic sufficient Suppose tables theorem theory true unbiased unknown variable X variance vector zero