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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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

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 31E

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Question

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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