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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Question

Give the following answers to three decimal places, where appropriate.
(c) Find the expected value of Y.
Answer:
(d) Find the variance of Y.
Answer:

Let X; be independent Uniform(-10,10) random variables, for i=1, 2, ..., 5.
Let
Y=X₁+X₂+...+X5.
(b) Find which of the following statements are correct for the moment generating function (mgf) My(t) of Y.
It is equal to the product of the mgfs of the Xi, for i=1,...,5
The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t.
It is equal to the sum of the mgfs of the Xi, for i=1,...,5
It is equal to 5 times the mgf of Xi, for some integer i between 1 and 5
It is equal to the mgf of any Xi to the power of 1/5, for i=1,...,5
It is equal to 10 times the mgf of any Xi to the power of 5, for some integer i between 1 and 5

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