## Introduction to Mathematical Statistics |

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### Contents

3 | 16 |

Unbiasedness Consistency and Limiting Distributions | 25 |

Multivariate Distributions | 73 |

Copyright | |

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approximate assume asymptotic best critical region complete sufficient statistic compute confidence interval Consider continuous random variable continuous type critical region defined deﬁnition degrees of freedom denote a random determine discussed equal equation Example Exercise Find ﬁrst gamma distribution given Hence hypothesis H0 independent random variables inequality integral joint pdf joint polf Let the random Let X1 likelihood function likelihood ratio test linear matrix median MVUE noncentral normal distribution null observations obtain order statistics p-value pdf f(x pdf or pmf Poisson distribution power function probability density functions proof quadratic form random sample random variables X1 random vector respectively sample mean sample space sequence Show sign test significance level simple hypothesis sufficient statistic Suppose t-distribution t-test test statistic Theorem unbiased estimator variance versus H1 Wilcoxon X1 and X2 zero elsewhere