Answered: Consider that X1, X2, X3, X4, X5 is an…

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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Consider that X1, X2, X3, X4, X5 is an independent random sample where Xi follows a normal distribution with a mean of 19 and a variance of 3.2, and Y1, Y2, Y3, Y4, Y5, Y6, Y7 is an independent random sample where Yi follows a normal ̅̅ distribution mean 27 and variance 4.1. Imagine we are interested in the sum of the two sample averages ? + ?. ̅̅ a) What is the mean and variance of ? + ?? Show your work. b) We know that the linear combination of normal random variables has a normal distribution. Using part a, what is the probability the sum of the two samples averages is less than 44?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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