# This could be called a variable length encoding of

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s underlined in this list. Let a∗ = 0.45043 · · · be such that the number in the k th decimal place of a∗ is one larger (modulo 10) than the number in the k th decimal place of ak . For any k ≥ 1, a∗ is not equal to ak because the numbers in their k th decimal places are diﬀerent. So a∗ is not on the list. So no list of numbers from the interval [0, 1] can contain all of the numbers from [0, 1]. Example 1.5.2 Example 1.2.3 describes the probability space (Ω, F , P ) for the experiment of selecting a point from the unit interval, [0, 1], such that the probability the outcome is in an interval [a, b] is b − a. This is true even if a = b, which means that the probability of any particular singleton subset {x} of [0, 1] is equal to zero. But the entire interval [0, 1] is the union of all such sets {x}, and those sets are mutually exclusive. Why then, doesn’t Axiom P.2 imply that P {Ω} = x∈Ω P {x} = 0, in contradiction to Axiom P.3? Solution: Axiom P.2 does not apply to this situation because the set [0, 1] is uncoun...
View Full Document

## This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

Ask a homework question - tutors are online