Let X1, X2, ..., Xn be independent random variables, Xi ∼ N(µi, σ2i), i = 1, ..., n. Show that Pn i=1 Xi is normally distributed with mean µ = Pni=1 µi and variance σ2 = Pni=1 σ2i. Use the convolution property. Let X1, X2, .., Xn be independent random variables, X; ~ N(ui, o}), i = 1, ..., n. Showthat 1 X; is normally distributed with mean µ = E-1Hi and variance o? = E=10.Use the convolution property.Li=1

Name: Let X1, X2, ..., Xn be independent random variables, Xi ∼ N(µi, σ2i),
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Description: Let X1, X2, ..., Xn be independent random variables, Xi ∼ N(µi, σ2i), i = 1, ..., n. Show that Pn i=1 Xi is normally distributed with mean µ = Pni=1 µi and variance σ2 = Pni=1 σ2i. Use the convolution property. Let X1, X2, .., Xn be independent rando

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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, ..., Xn be independent random variables, Xi ∼ N(µi, σ2i), i = 1, ..., n. Show that Pn i=1 Xi is normally distributed with mean µ = Pni=1 µi and variance σ2 = Pni=1 σ2i. Use the convolution property.

Let X1, X2, .., Xn be independent random variables, X; ~ N(ui, o}), i = 1, ..., n. Show
that 1 X; is normally distributed with mean µ = E-1Hi and variance o? = E=10.
Use the convolution property.
Li=1

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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