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Let X be a Uniform(-9,9) random variable. (a) The moment generating function of X is Mx(t) = A(eBt – ect) £, 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)? 0.06, -9, 9, 1 4.50, -9, 9, -1 0.06, 9, -9, -1 0.22, 9, -9, -1 O 4.50, 9, -9, -1 O 0.229,-9, 1 O O

Let X be a Uniform(-9,9) random variable. (a) The moment generating function of X is Mx(t) = A(eBt – ect) £, 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)? 0.06, -9, 9, 1 4.50, -9, 9, -1 0.06, 9, -9, -1 0.22, 9, -9, -1 O 4.50, 9, -9, -1 O 0.229,-9, 1 O O

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 43CR
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Let X be a Uniform(-9,9) random variable. (a) The moment generating function of X is Mx(t) = A(e³t – ect) £, 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)? 0.06, -9, 9, 1 O 4.50, -9, 9, -1 0.06, 9, -9, -1 0.22, 9, -9, -1 4.50, 9, -9, -1 0.22 9, -9, 1
Transcribed Image Text:Let X be a Uniform(-9,9) random variable. (a) The moment generating function of X is Mx(t) = A(e³t – ect) £, 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)? 0.06, -9, 9, 1 O 4.50, -9, 9, -1 0.06, 9, -9, -1 0.22, 9, -9, -1 4.50, 9, -9, -1 0.22 9, -9, 1
Let X; be independent Uniform(-9,9) 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. It is equal to the sum of the mgfs of the Xi, for i=1,...,14 It is equal to the product of the mgfs of the Xi, for i=1,...,14 OIt is equal to the mgf of any Xi to the power of 1/14, for i=1,...,14 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14 It is equal to 9 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(-9,9) 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. It is equal to the sum of the mgfs of the Xi, for i=1,...,14 It is equal to the product of the mgfs of the Xi, for i=1,...,14 OIt is equal to the mgf of any Xi to the power of 1/14, for i=1,...,14 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14 It is equal to 9 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14
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