## An Introduction to Probability Theory and Mathematical StatisticsSets and classes; Calculus; Linear Algebra; Probability; Random variables and their probability distributions; Moments and generating functions; Random vectors; Some special distributions; Limit theorems; Sample moments and their distributions; The theory of point estimation; Neyman-pearson theory of testing of hypotheses; Some further results on hypotheses testing; Confidence estimation; The general linear hypothesis; nonparametric statistical inference; Sequential statistical inference. |

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### Contents

Sets and Classes | 1 |

Linear Algebra | 15 |

Random Variables and Their Probability Distributions | 52 |

Copyright | |

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### Common terms and phrases

a₁ accept alternative assume bound called choose Clearly common complete compute conditional confidence interval constant continuous converges Corollary defined Definition determined distribution equal estimate event Example exists Find finite fixed fo(x follows function given H₁ holds hypothesis independent inequality integer joint known least Lemma length Let X1 likelihood mean method minimizes normal Note null observations obtained otherwise P₁ parameter population positive possible probability problem procedure Proof Prove random ratio reject Remark respectively result rv's sample satisfies sequence sequential Similarly space squares statistic sufficient Suppose Table Theorem unbiased estimate unknown values variable variance vector write X₁ Y₁ Σ Σ