Let X be a Uniform(-5,5) random variable. (a) The moment generating function of X is Mx(t) = A(et - ect), for some t in the neighbourhood of zero. Which values of the constants A, B, C, D are correct (following the same order as they occur here)? ○ 0.10, -5, 5, 1 0.10, 5, -5, -1 0.40,5, -5, -1 ○ 0.405,-5,1 2.50, -5, 5, -1 2.50, 5, -5, -1 Clear my choice Let X; be independent Uniform(-5,5) random variables, for i=1, 2, ..., 5. Let Y=X1+X2+...+X5. (b) Find which of the following statements are correct for the moment generating function (mgf) My(t) of Y. It is equal to the mgf of any Xi to the power of 1/5, for i=1,...,5 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to 5 times the mgf of Xi, for some integer i between 1 and 5 It is equal to the product of the mgfs of the Xi, for i=1,...,5 It is equal to 5 times the mgf of any Xi to the power of 5, for some integer i between 1 and 5 It is equal to the sum of the mgfs of the Xi, for i=1,...,5 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 a Uniform(-5,5) random variable. (a) The moment generating function of X is Mx(t) = A(et - ect), for some t in the neighbourhood of zero. Which values of the constants A, B, C, D are correct (following the same order as they occur here)? ○ 0.10, -5, 5, 1 0.10, 5, -5, -1 0.40,5, -5, -1 ○ 0.405,-5,1 2.50, -5, 5, -1 2.50, 5, -5, -1 Clear my choice Let X; be independent Uniform(-5,5) random variables, for i=1, 2, ..., 5. Let Y=X1+X2+...+X5. (b) Find which of the following statements are correct for the moment generating function (mgf) My(t) of Y. It is equal to the mgf of any Xi to the power of 1/5, for i=1,...,5 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to 5 times the mgf of Xi, for some integer i between 1 and 5 It is equal to the product of the mgfs of the Xi, for i=1,...,5 It is equal to 5 times the mgf of any Xi to the power of 5, for some integer i between 1 and 5 It is equal to the sum of the mgfs of the Xi, for i=1,...,5 Give the following answers to three decimal places, where appropriate. (c) Find the expected value of Y. (d) Find the variance of Y.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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