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ADVANCED PROBABILITY AND STATISTICAL INFERENCE I

ADVANCED PROBABILITY ANDSTATISTICAL INFERENCE ILecture Notes of BIOS 760 Distribution of Normalized Summation Uniform Random VariablesPREFACET hese course notes have been revised based on my past teaching experience at the departmentof Biostatistics in the University of North Carolina in Fall 2004 and Fall 2005. The context in-cludes distribution theory , PROBABILITY and measure theory , large sample theory , theory of pointestimation and efficiency theory . The last chapter specially focuses on maximum likelihoodapproach. Knowledge of fundamental real analysis and STATISTICAL INFERENCE will be helpful forreading these parts of the notes are compiled with moderate changes based on two valuable textbooks: theory of Point Estimation(second edition, Lehmann and Casella, 1998) andA Course inLarge Sample theory (Ferguson, 2002).

ADVANCED PROBABILITY AND STATISTICAL INFERENCE I Lecture Notes of BIOS 760-4 -2 0 2 4 0 50 100 150 200 250 300 350 400 n=1 ... cludes distribution theory, probability and measure theory, large sample theory, theory of point ... probability mass function or a joint density function. For example, we can de ne the mean

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