Let X; be independent Uniform(-7,7) random variables, for i=1, 2, ..., 7. Let Y=X₁+X₂+...+X7. (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 mgf of any Xi to the power of 1/7, for i=1,...,7 It is equal to the product of the mgfs of the Xi, for i=1,...,7 It is equal to the sum of the mgfs of the Xi, for i=1,...,7 It is equal to 7 times the mgf of Xi, for some integer i between 1 and 7 It is equal to 7 times the mgf of any Xi to the power of 7, for some integer i between 1 and 7
Let X; be independent Uniform(-7,7) random variables, for i=1, 2, ..., 7. Let Y=X₁+X₂+...+X7. (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 mgf of any Xi to the power of 1/7, for i=1,...,7 It is equal to the product of the mgfs of the Xi, for i=1,...,7 It is equal to the sum of the mgfs of the Xi, for i=1,...,7 It is equal to 7 times the mgf of Xi, for some integer i between 1 and 7 It is equal to 7 times the mgf of any Xi to the power of 7, for some integer i between 1 and 7
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let X be a Uniform(-7,7) random variable.
(a) The moment generating function of X is Mx(t) = A(eBt - ect) t, for some tin the neighbourhood of zero.
Which values of the constants A, B, C, D are correct (following the same order as they occur here)?
3.50, -7, 7, -1
3.50, 7, -7, -1
O 0.29 7, -7,1
0.07, 7, -7, -1
0.07, -7, 7, 1
0.29, 7, -7, -1
Transcribed Image Text:Let X; be independent Uniform(-7,7) random variables, for i=1, 2, ..., 7.
Let
Y=X₁+X₂+...+X7.
(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 mgf of any Xi to the power of 1/7, for i=1,...,7
It is equal to the product of the mgfs of the Xi, for i=1,...,7
It is equal to the sum of the mgfs of the Xi, for i=1,...,7
It is equal to 7 times the mgf of Xi, for some integer i between 1 and 7
It is equal to 7 times the mgf of any Xi to the power of 7, for some integer i between 1 and 7
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