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13. For each of the collections of the subsets of 2 = {W1, W2, W3, W4} set out below, state whether it is a σ-algebra. If it is not, explain why. (a) F₁ = P(N). (b) F₂ = {0, N}. (c) F3 = {0, {w1}, {W2, W3}, {w₁}, }. (d) F₁ = {0, {w1}, {W2, W3, W1}, N}. 14. Let N = {w1, W2, W3, W1}. A random variance X : → R has X = 1 in state wi 3 in state W3 -2 in states W2, W4 Let F = {0, {w1, w₂}, {w3, W₁}, }. (a) Is F is a σ-algebra? Give a brief explanation for your answer. (b) Is X F-measurable? Give a brief explanation for your answer.

13. For each of the collections of the subsets of 2 = {W1, W2, W3, W4} set out below, state whether it is a σ-algebra. If it is not, explain why. (a) F₁ = P(N). (b) F₂ = {0, N}. (c) F3 = {0, {w1}, {W2, W3}, {w₁}, }. (d) F₁ = {0, {w1}, {W2, W3, W1}, N}. 14. Let N = {w1, W2, W3, W1}. A random variance X : → R has X = 1 in state wi 3 in state W3 -2 in states W2, W4 Let F = {0, {w1, w₂}, {w3, W₁}, }. (a) Is F is a σ-algebra? Give a brief explanation for your answer. (b) Is X F-measurable? Give a brief explanation for your answer.

Principles Of Marketing
Principles Of Marketing
17th Edition
ISBN:9780134492513
Author:Kotler, Philip, Armstrong, Gary (gary M.)
Publisher:Kotler, Philip, Armstrong, Gary (gary M.)
Chapter1: Marketing: Creating Customer Value And Engagement
Section: Chapter Questions
Problem 1.1DQ
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13. For each of the collections of the subsets of 2 = {W1, W2, W3, W4} set out below, state whether it is a σ-algebra. If it is not, explain why. (a) F₁ = P(N). (b) F₂ = {0, N}. (c) F3 = {0, {w1}, {W2, W3}, {w₁}, }. (d) F₁ = {0, {w1}, {W2, W3, W1}, N}. 14. Let N = {w1, W2, W3, W1}. A random variance X : → R has X = 1 in state wi 3 in state W3 -2 in states W2, W4 Let F = {0, {w1, w₂}, {w3, W₁}, }. (a) Is F is a σ-algebra? Give a brief explanation for your answer. (b) Is X F-measurable? Give a brief explanation for your answer.
Transcribed Image Text:13. For each of the collections of the subsets of 2 = {W1, W2, W3, W4} set out below, state whether it is a σ-algebra. If it is not, explain why. (a) F₁ = P(N). (b) F₂ = {0, N}. (c) F3 = {0, {w1}, {W2, W3}, {w₁}, }. (d) F₁ = {0, {w1}, {W2, W3, W1}, N}. 14. Let N = {w1, W2, W3, W1}. A random variance X : → R has X = 1 in state wi 3 in state W3 -2 in states W2, W4 Let F = {0, {w1, w₂}, {w3, W₁}, }. (a) Is F is a σ-algebra? Give a brief explanation for your answer. (b) Is X F-measurable? Give a brief explanation for your answer.
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