## A Course in Mathematical StatisticsA Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference.* Contains 25% new material * Includes the most complete coverage of sufficiency * Transformation of Random Vectors * Sufficiency / Completeness / Exponential Families * Order Statistics * Elements of Nonparametric Density Estimation * Analysis of Variance (ANOVA) * Regression Analysis * Linear Models |

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### Contents

1 | |

14 | |

Chapter 3 On Random Variables and Their Distributions | 53 |

Chapter 4 Distribution Functions Probability Densities and Their Relationship | 85 |

Chapter 5 Moments of Random VariablesSome Moment and Probability Inequalities | 106 |

Chapter 6 Characteristic Functions Moment Generating Functions and Related Theorems | 138 |

Chapter 7 Stochastic Independence with Some Applications | 164 |

Chapter 8 Basic Limit Theorems | 180 |

Chapter 15 Confidence RegionsTolerance Intervals | 397 |

Chapter 16 The General Linear Hypothesis | 416 |

Chapter 17 Analysis of Variance | 440 |

Chapter 18 The Multivariate Normal Distribution | 463 |

Chapter 19 Quadratic Forms | 476 |

Chapter 20 Nonparametric Inference | 485 |

Appendix I Topics from Vector and Matrix Algebra | 499 |

Appendix II Noncentral t X2 and FDistributions | 508 |

Chapter 9 Transformations of Random Variables and Random Vectors | 212 |

Chapter 10 Order Statistics and Related Theorems | 245 |

Chapter 11 Sufficiency and Related Theorems | 259 |

Chapter 12 Point Estimation | 284 |

Chapter 13 Testing Hypotheses | 327 |

Chapter 14 Sequential Procedures | 382 |

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