Let Xi be independent Uniform(−6,6) random variables, for i=1, 2, ..., 13. Let Y = X1+X2+...+X13 . (b) Find which of the following statements are correct for the moment generating function (mgf) MY(t) of Y. A The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. B It is equal to the sum of the mgfs of the Xi, for i=1,...,13 C It is equal to the mgf of any Xi to the power of 1/13, for i=1,...,13 D It is equal to 6 times the mgf of any Xi to the power of 13, for some integer i between 1 and 13 E It is equal to 13 times the mgf of Xi, for some integer i between 1 and 13 F It is equal to the product of the mgfs of the Xi, for i=1,...,13 (c) Find the expected value of Y. (d) Find the variance of Y.
Let Xi be independent Uniform(−6,6) random variables, for i=1, 2, ..., 13. Let Y = X1+X2+...+X13 . (b) Find which of the following statements are correct for the moment generating function (mgf) MY(t) of Y. A The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. B It is equal to the sum of the mgfs of the Xi, for i=1,...,13 C It is equal to the mgf of any Xi to the power of 1/13, for i=1,...,13 D It is equal to 6 times the mgf of any Xi to the power of 13, for some integer i between 1 and 13 E It is equal to 13 times the mgf of Xi, for some integer i between 1 and 13 F It is equal to the product of the mgfs of the Xi, for i=1,...,13 (c) Find the expected value of Y. (d) Find the variance of Y.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 1CR
Related questions
Question
Let Xi be independent Uniform(−6,6) random variables, for i=1, 2, ..., 13.
Let Y = X1+X2+...+X13 .
(b) Find which of the following statements are correct for the moment generating
A The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t.
B It is equal to the sum of the mgfs of the Xi, for i=1,...,13
C It is equal to the mgf of any Xi to the power of 1/13, for i=1,...,13
D It is equal to 6 times the mgf of any Xi to the power of 13, for some integer i between 1 and 13
E It is equal to 13 times the mgf of Xi, for some integer i between 1 and 13
F It is equal to the product of the mgfs of the Xi, for i=1,...,13
(c) Find the
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