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 mgf of any Xi to the power of 1/5, for i=1,...,5 It is equal to the sum of the mgfs of the Xi, 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 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to 5 times the mgf of Xi, for some integer i between 1 and 5 It is equal to the product of the mgfs of the Xi, for i=1,...,5
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 mgf of any Xi to the power of 1/5, for i=1,...,5 It is equal to the sum of the mgfs of the Xi, 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 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to 5 times the mgf of Xi, for some integer i between 1 and 5 It is equal to the product of the mgfs of the Xi, for i=1,...,5
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(d) Find the variance of Y.
Transcribed Image Text: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 mgf of any Xi to the power of 1/5, for i=1,...,5
It is equal to the sum of the mgfs of the Xi, 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
The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t.
It is equal to 5 times the mgf of Xi, for some integer i between 1 and 5
It is equal to the product of the mgfs of the Xi, for i=1,...,5
Transcribed Image Text:Give the following answers to three decimal places, where appropriate.
(c) Find the expected value of Y.
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