Expected value of a sampling estimate

ALTHOUGH SOME PROOFS ARE PRESENTED, THE EMPHASIS IS MORE ON EXPOSITION OF MATHEMATICAL LANGUAGE AND CONCEPTS THAN ON THE MATHEMATICS PER SE AND RIGOROUS PROOFS. MANY PROBLEMS ARE GIVEN AS EXERCISES SO A STUDENT MAY TEST HIS INTERPRETATION OR UNDERSTANDING OF THE CONCEPTS. EACH CHAPTER BEGINS WITH VERY SIMPLE EXPLANATIONS AND ENDS AT A MUCH MORE ADVANCED LEVEL. CHAPTERS I AND II PROVIDE A BACKGROUND FOR CHAPTER III, WHICH IS A DISCUSSION OF EXPECTED VALUES OF RANDOM VARIABLES AND THE ORIGINAL PURPOSE OF THIS MONOGRAPH. FINALLY, CHAPTER IV FOCUSES ATTENTION ON THE DISTRIBUTION OF AN ESTIMATE WHICH IS THE BASIS FOR COMPARING THE ACCURACY OF ALTERNATIVE SAMPLING PLANS AS WELL AS A BASIS FOR STATEMENTS ABOUT THE ACCURACY OF AN ESTIMATE FROM A SAMPLE.