Let X; be independent Uniform(-6,6) random variables, for i=1, 2, ., 14. Let Y = X1+X2+...+X14 - (b) Find which of the following statements are correct for the moment generating function (mgf) My{t) of Y. O Itis equal to the sum of the mgfs of the Xi, for i=1,..,14 O Itis equal to the mgf of any Xi to the power of 1/14, for i=1,.,14 O The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. O Itis equal to 6 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14 O Itis equal to 14 times the mgf of Xi, for some integer i between 1 and 14 O Itis equal to the product of the mgfs of the Xi, for i=1,.,14 Give the following answers to three decimal places, where appropriate. (c) Find the expected value of Y. (d) Find the variance of Y.
Let X; be independent Uniform(-6,6) random variables, for i=1, 2, ., 14. Let Y = X1+X2+...+X14 - (b) Find which of the following statements are correct for the moment generating function (mgf) My{t) of Y. O Itis equal to the sum of the mgfs of the Xi, for i=1,..,14 O Itis equal to the mgf of any Xi to the power of 1/14, for i=1,.,14 O The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. O Itis equal to 6 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14 O Itis equal to 14 times the mgf of Xi, for some integer i between 1 and 14 O Itis equal to the product of the mgfs of the Xi, for i=1,.,14 Give the following answers to three decimal places, where appropriate. (c) Find the expected value of Y. (d) Find the variance of Y.
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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Transcribed Image Text:Let X; be independent Uniform(-6,6) random variables, for i=1, 2, ., 14.
Let Y = X1+X2+...+X14 -
(b) Find which of the following statements are correct for the moment generating function (mgf) My{t) of Y.
O Itis equal to the sum of the mgfs of the Xi, for i=1,..,14
O Itis equal to the mgf of any Xi to the power of 1/14, for i=1,.,14
O The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t.
O Itis equal to 6 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14
O Itis equal to 14 times the mgf of Xi, for some integer i between 1 and 14
O Itis equal to the product of the mgfs of the Xi, for i=1,.,14
Give the following answers to three decimal places, where appropriate.
(c) Find the expected value of Y.
(d) Find the variance of Y.
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