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Let X; be independent Uniform(-5,5) 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. 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,...,14 It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14 It is equal to the product of the mgfs of the Xi, for i=1,...,14 O It is equal to the mgf of any Xi to the power of 1/14, for i=1,...,14 It is equal to 5 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14

Let X; be independent Uniform(-5,5) 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. 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,...,14 It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14 It is equal to the product of the mgfs of the Xi, for i=1,...,14 O It is equal to the mgf of any Xi to the power of 1/14, for i=1,...,14 It is equal to 5 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14

Calculus For The Life Sciences
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
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Let X; be independent Uniform(-5,5) 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. 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,...,14 It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14 It is equal to the product of the mgfs of the Xi, for i=1,...,14 O It is equal to the mgf of any Xi to the power of 1/14, for i=1,...,14 It is equal to 5 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14
Transcribed Image Text:Let X; be independent Uniform(-5,5) 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. 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,...,14 It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14 It is equal to the product of the mgfs of the Xi, for i=1,...,14 O It is equal to the mgf of any Xi to the power of 1/14, for i=1,...,14 It is equal to 5 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14
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