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Examples and Problems in Mathematical Statistics by Shelemyahu Zacks

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CHAPTER 1

Basic Probability Theory

PART I: THEORY

It is assumed that the reader has had a course in elementary probability. In this chapter we discuss more advanced material, which is required for further developments.

1.1 OPERATIONS ON SETS

Let inline denote a sample space. Let E1, E2 be subsets of inline. We denote the union by E1 inline E2 and the intersection by E1 inline E2. inline = inlineE denotes the complement of E. By DeMorgan’s laws inline = inline1 inline inline2 and = 1 2.

Given a sequence of sets {En, n ≥ 1} (finite or infinite), we define ...

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