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Exercises and Solutions in Biostatistical Theory

Lawrence L. Kupper, Brian H. Neelon, and Sean M. O'Brien
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
Texts in Statistical Science
Problem Book
We do not plan to review this book.

Basic Probability Theory
Counting Formulas (N-tuples, permutations, combinations, Pascal’s identity, Vandermonde’s identity)
Probability Formulas (union, intersection, complement, mutually exclusive events, conditional probability, independence, partitions, Bayes’ theorem)

Univariate Distribution Theory
Discrete and Continuous Random Variables
Cumulative Distribution Functions
Median and Mode
Expectation Theory
Some Important Expectations (mean, variance, moments, moment generating function, probability generating function)
Inequalities Involving Expectations
Some Important Probability Distributions for Discrete Random Variables
Some Important Distributions (i.e., Density Functions) for Continuous Random Variables

Multivariate Distribution Theory
Discrete and Continuous Multivariate Distributions
Multivariate Cumulative Distribution Functions
Expectation Theory (covariance, correlation, moment generating function)
Marginal Distributions
Conditional Distributions and Expectations
Mutual Independence among a Set of Random Variables
Random Sample
Some Important Multivariate Discrete and Continuous Probability Distributions
Special Topics of Interest (mean and variance of a linear function, convergence in distribution and the Central Limit Theorem, order statistics, transformations)

Estimation Theory
Point Estimation of Population Parameters (method of moments, unweighted and weighted least squares, maximum likelihood)
Data Reduction and Joint Sufficiency (Factorization Theorem)
Methods for Evaluating the Properties of a Point Estimator (mean-squared error, Cramér–Rao lower bound, efficiency, completeness, Rao–Blackwell theorem)
Interval Estimation of Population Parameters (normal distribution-based exact intervals, Slutsky’s theorem, consistency, maximum-likelihood-based approximate intervals)

Hypothesis Testing Theory
Basic Principles (simple and composite hypotheses, null and alternative hypotheses, Type I and Type II errors, power, P-value)
Most Powerful (MP) and Uniformly Most Powerful (UMP) Tests (Neyman–Pearson Lemma)
Large-Sample ML-Based Methods for Testing a Simple Null Hypothesis versus a Composite Alternative Hypothesis (likelihood ratio, Wald, and score tests)
Large-Sample ML-Based Methods for Testing a Composite Null Hypothesis versus a Composite Alternative Hypothesis (likelihood ratio, Wald, and score tests)

Appendix: Useful Mathematical Results