What is the moment generating function of the sample mean?

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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a) Mr Sepuru, a statistics class representative, during a Wednesday lecture at 11:10
decided to let X₁, X2,..., X10 to be the observations from a random sample of size
10 from a distribution with density
f(x)=√2π
e²7²₁-00<x
-∞0 < x < 80
elsewhere
and ask his fellow students to answer the following questions.
i) What is the moment generating function of the sample mean?
ii) What will be the mean of the sample mean?
iii) Show that the variance of the sample mean is 0.1.
Transcribed Image Text:a) Mr Sepuru, a statistics class representative, during a Wednesday lecture at 11:10 decided to let X₁, X2,..., X10 to be the observations from a random sample of size 10 from a distribution with density f(x)=√2π e²7²₁-00<x -∞0 < x < 80 elsewhere and ask his fellow students to answer the following questions. i) What is the moment generating function of the sample mean? ii) What will be the mean of the sample mean? iii) Show that the variance of the sample mean is 0.1.
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