et X be a Uniform(-5,5) 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)? 2.50, -5, 5, -1 2.50, 5, -5, -1 0.40 5, -5, 1 0.10, -5, 5, 1 0.10, 5, -5, -1 0.40, 5, -5, -1 Let X; be independent Uniform(-5,5) random variables, for i=1, 2, ..., 8. Let Y=X₁+X₂+...+Xg. (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,...,8 It is equal to the mgf of any Xi to the power of 1/8, for i=1,...,8 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to 8 times the mgf of Xi, for some integer i between 1 and 8 It is equal to 5 times the mgf of any Xi to the power of 8, for some integer i between 1 and 8 It is equal to the product of the mgfs of the Xi, for i=1,...,8 Give the following answers to three decimal places, where appropriate. (c) Find the expected value of Y. Answer: (d) Find the variance of Y. Answer:

et X be a Uniform(-5,5) 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)? 2.50, -5, 5, -1 2.50, 5, -5, -1 0.40 5, -5, 1 0.10, -5, 5, 1 0.10, 5, -5, -1 0.40, 5, -5, -1 Let X; be independent Uniform(-5,5) random variables, for i=1, 2, ..., 8. Let Y=X₁+X₂+...+Xg. (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,...,8 It is equal to the mgf of any Xi to the power of 1/8, for i=1,...,8 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to 8 times the mgf of Xi, for some integer i between 1 and 8 It is equal to 5 times the mgf of any Xi to the power of 8, for some integer i between 1 and 8 It is equal to the product of the mgfs of the Xi, for i=1,...,8 Give the following answers to three decimal places, where appropriate. (c) Find the expected value of Y. Answer: (d) Find the variance of Y. Answer:

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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