x is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the standard deviation , and Fx(X) refers to the cumulative distribution function CDF. It is known that Fx(-4.8) = 0.500 and Fx(1.4)=0.977, what value of Xo do we find the probability Fx(Xo) = P(X<Xo) = 0.159 ? ( Ans = -7.9) The Normal Distribution is represented as a symmetrical, bell-shaped curve centered around the mean (\(\overline{X}\)). The x-axis denotes values, and the y-axis shows probability.### Key Features:- **Center**: The curve is highest at the mean (\(\overline{X}\)).- **Symmetry**: The distribution is symmetric about the mean.- **Tails**: The tails of the distribution extend infinitely, approaching but never touching the x-axis.### Probability and Standard Deviations:- **-1.96σ to +1.96σ**: Approximately 95% of the values fall within this range.- **-2.58σ to +2.58σ**: Around 99% of the values are within this range.### Probability of Cases:- **Outside ±3σ**: Probability is approximately 0.0013.- **Between ±2σ to ±3σ**: Probability is around 0.0214.- **Between ±1σ to ±2σ**: Probability is approximately 0.1359.- **Between 0σ and ±1σ**: Probability is about 0.3413.### Cumulative Percentages:- **±1σ**: Accounts for 68.3% of the data.- **±2σ**: Accounts for 95.5% of the data.- **±3σ**: Covers about 99.7% of the data.### Z Scores and T Scores:The x-axis also shows corresponding Z scores and T scores for each standard deviation, ranging from -4.0 to +4.0.This graph is essential for understanding data distributions, calculating probabilities, and performing statistical analyses in various fields.

Let x be a Gaussian random variable,Let μμ denote the mean and σσ denote the standard deviation Let…

x is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the standard deviation , and Fx(X) refers to the cumulative distribution function CDF. It is known that Fx(-4.8) = 0.500 and Fx(1.4)=0.977, what value of Xo do we find the probability Fx(Xo) = P(X

x is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the standard deviation , and Fx(X) refers to the cumulative distribution function CDF. It is known that Fx(-4.8) = 0.500 and Fx(1.4)=0.977, what value of Xo do we find the probability Fx(Xo) = P(X

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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