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.

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.

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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Question

(d) Find the variance of Y.

Let X be a Uniform(–7,7) random variable.
(a) The moment generating function of X is Mx(t) = A(eBt - 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)?
0.07, -7, 7, 1
0.29, 7, -7, -1
0.07, 7, -7, -1
3.50, -7, 7, -1
3.50, 7, -7, -1
0.29 7, -7, 1

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.
It is equal to the product of the mgfs of the Xi, for i=1,...,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
It is equal to the mgf of any Xi to the power of 1/7, 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
The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t.

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