Tucker H.G. Mathematical methods in sample surveys

World Scientific, 1998. — 208 p.
This book is about both the mathematics of sample surveys and about sample surveys. The mathematics is both elementary and rigorous. It is suitable for a one year junior-senior level course for mathematics and statistics majors as well as for students in the social sciences who are not handicapped by a fear of proofs in mathematics. It requires no previous knowledge of statistics, and it could actually serve as an introduction to statistics. A sizeable part of the book covers the discrete probability needed for the sampling methods covered. Topics then covered are: simple random sampling, sampling with unequal probabilities, linear relationships, stratified sampling, cluster sampling and two-stage sampling.Events and Probability
Random Variables
Expectation
Conditional Expectation
Limit Theorems
Simple Random Sampling
Unequal Probability Sampling
Linear Relationships
Stratified Sampling
Cluster Sampling
Two-Stage Sampling