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EXERCISE 5 Suppose that X1,·,Xm and Y1, , Yn are two samples, with X; between the sample means, X – Ỹ, is then a linear combination of m +n normal random variables. All the random variables are independent. Answer the following questions: N(u1,01) and Y; ~ N(u2, 02). The difference a. Use moment generating functions to show that X - Ý follows a normal distribution. Find the mean and variance of this distribution. b. Suppose oi = 2, o = 2.5, and m = n. Find the sample size n so that X - Y will be within one unit of µi – µ2 with probability 0.95.

EXERCISE 5 Suppose that X1,·,Xm and Y1, , Yn are two samples, with X; between the sample means, X – Ỹ, is then a linear combination of m +n normal random variables. All the random variables are independent. Answer the following questions: N(u1,01) and Y; ~ N(u2, 02). The difference a. Use moment generating functions to show that X - Ý follows a normal distribution. Find the mean and variance of this distribution. b. Suppose oi = 2, o = 2.5, and m = n. Find the sample size n so that X - Y will be within one unit of µi – µ2 with probability 0.95.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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EXERCISE 5 Suppose that X1,·, Xm and Y1, ., Yn are two samples, with X; - between the sample means, X – Ý, is then a linear combination of m +n normal random variables. All the random variables are independent. Answer the following questions: Ν(μ1, σι) and Y N(u2, 02). The difference a. Use moment generating functions to show that X variance of this distribution. Y follows a normal distribution. Find the mean and - b. Suppose o = 2, o% = 2.5, and m = n. Find the sample size n so that X - Ý will be within one unit of µi with probability 0.95.
Transcribed Image Text:EXERCISE 5 Suppose that X1,·, Xm and Y1, ., Yn are two samples, with X; - between the sample means, X – Ý, is then a linear combination of m +n normal random variables. All the random variables are independent. Answer the following questions: Ν(μ1, σι) and Y N(u2, 02). The difference a. Use moment generating functions to show that X variance of this distribution. Y follows a normal distribution. Find the mean and - b. Suppose o = 2, o% = 2.5, and m = n. Find the sample size n so that X - Ý will be within one unit of µi with probability 0.95.
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We have to use moment generating function to prove that difference between sample mean of two normal population is also normal .

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