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Suppose that x,, X, ..., X and Y,, Y,, ..., Y, are independent random samples, with the variables x, normally distributed with mean u, and variance o,? and the variables Y, normally distributed with mean , and variance o,. The difference between the sample means, X - Y, is then a linear combination of m +n normally distributed random variables and, by this theorem, is itself normally distributed. (a) Find EX - (b) Find VX - ). (c) Suppose that o,? = 3, , = 6.5, and m = n. Find the minimum sample sizes so that (X -Y) will be within 1 unit of (4, - 42) with probability 0.95. (Round your answer up to the nearest integer.) m=n= You may need to use the appropriate appendix table technology to answer this question.

Suppose that x,, X, ..., X and Y,, Y,, ..., Y, are independent random samples, with the variables x, normally distributed with mean u, and variance o,? and the variables Y, normally distributed with mean , and variance o,. The difference between the sample means, X - Y, is then a linear combination of m +n normally distributed random variables and, by this theorem, is itself normally distributed. (a) Find EX - (b) Find VX - ). (c) Suppose that o,? = 3, , = 6.5, and m = n. Find the minimum sample sizes so that (X -Y) will be within 1 unit of (4, - 42) with probability 0.95. (Round your answer up to the nearest integer.) m=n= You may need to use the appropriate appendix table technology to answer this question.

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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Suppose that x,, X2, ..., Xm and Y,, Y2, ..., Y, are independent random samples, with the variables X, normally distributed with mean µ, and variance o, means, X - Y, is then a linear combination of m + n normally distributed random variables and, by this theorem, is itself normally distributed. and the variables Y, normally distributed with mean u, and variance o,2. The difference between the sample (a) Find E(X - ). (b) Find V(X - ). (c) Suppose that o, = 3, o, = 6.5, and m = n. Find the minimum sample sizes so that (X - Y) will be within 1 unit of (u, - µ,) with probability 0.95. (Round your answer up to the nearest integer.) m = n = You may need to use the appropriate appendix table or technology to answer this question.
Transcribed Image Text:Suppose that x,, X2, ..., Xm and Y,, Y2, ..., Y, are independent random samples, with the variables X, normally distributed with mean µ, and variance o, means, X - Y, is then a linear combination of m + n normally distributed random variables and, by this theorem, is itself normally distributed. and the variables Y, normally distributed with mean u, and variance o,2. The difference between the sample (a) Find E(X - ). (b) Find V(X - ). (c) Suppose that o, = 3, o, = 6.5, and m = n. Find the minimum sample sizes so that (X - Y) will be within 1 unit of (u, - µ,) with probability 0.95. (Round your answer up to the nearest integer.) m = n = You may need to use the appropriate appendix table or technology to answer this question.
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