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Exercise 5. Let X be a r.v. representing the outcome of rolling a fair, 6-sided die: f(1) = ƒ(2) = - = f(6) = 1/6. (a) Verify explicitly that E(X) = 3.5. (b) Calculate E(X²), and verify that E(X²) is not the same as the square of E(X).

Exercise 5. Let X be a r.v. representing the outcome of rolling a fair, 6-sided die: f(1) = ƒ(2) = - = f(6) = 1/6. (a) Verify explicitly that E(X) = 3.5. (b) Calculate E(X²), and verify that E(X²) is not the same as the square of E(X).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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Exercise 5. Let X be a r.v. representing the outcome of rolling a fair, 6-sided die: ƒ(1) = ƒ(2) = = = f(6) = 1/6. (a) Verify explicitly that E(X) = 3.5. (b) Calculate E(X²), and verify that E(X²) is not the same as the square of E(X).
Transcribed Image Text:Exercise 5. Let X be a r.v. representing the outcome of rolling a fair, 6-sided die: ƒ(1) = ƒ(2) = = = f(6) = 1/6. (a) Verify explicitly that E(X) = 3.5. (b) Calculate E(X²), and verify that E(X²) is not the same as the square of E(X).
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