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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Question

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.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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