Let X1, X2,...Xn be a random sample of size n from a normal distribution with mean u and variance o2. Let Xn denote the sample average, defined in the usual way. PROVE Var [Xn] = o2 / n

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Answered: Let X1, X2,...Xn be a random sample of…

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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Let X₁, X₂,...X_nbe a random sample of size n from a normal distribution with mean u and variance o². Let X_ndenote the sample average, defined in the usual way.

PROVE

Var [X_n] = o² / n

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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