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PLOT-B X<-seq(-4,8,0.01) y <-dnorm(x, 2.2,1.9) plot(x,y,type = "1") polygon(c(x[x< 1], 1),c(y[x< 1],y[x = = -4]),col = "honeydew2")

PLOT-B X<-seq(-4,8,0.01) y <-dnorm(x, 2.2,1.9) plot(x,y,type = "1") polygon(c(x[x< 1], 1),c(y[x< 1],y[x = = -4]),col = "honeydew2")

MATLAB: An Introduction with Applications
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

There are two Gaussian curves below (Plots A and B), along with the respective R source codes.
Looking at the plots and the source codes provided, identify the parameters of respective 
Gaussian pdf's (probability density functions) and the numeric value of x in the PDF F(x)
express the areas under the curves in terms of F(x). ( Do not calculate those areas.Your answers must be like F(x) or 1- F(x)  for a relevant value of x.) 

Below is the source code and image for part B

**Normal Distribution with Highlighted Area** This graph represents a normal distribution curve, also known as a bell curve, which is a common way to represent data in statistics. The x-axis is labeled as "x" and ranges from -4 to 8. The y-axis is labeled as "y" and ranges from 0.00 to 0.20. ### Key Features: - **Curve Shape**: The curve peaks at the center and tapers off symmetrically on both sides, illustrating the probability density function of a normal distribution. - **Highlighted Area**: A portion of the graph is shaded in light green from the left side (around x = -4) to approximately x = 1.5. This shaded region represents the probability or proportion of data falling between these x-values. ### Educational Insights: - The highest point of the curve represents the mean of the data. - The shaded area could be used to show the probability of a random variable falling within a certain range, often used to calculate z-scores or critical values. - Understanding how to interpret this graph is essential in fields like statistics, research, and data analysis. This visual tool is valuable for those studying statistical methods and probability theory.
Transcribed Image Text:**Normal Distribution with Highlighted Area** This graph represents a normal distribution curve, also known as a bell curve, which is a common way to represent data in statistics. The x-axis is labeled as "x" and ranges from -4 to 8. The y-axis is labeled as "y" and ranges from 0.00 to 0.20. ### Key Features: - **Curve Shape**: The curve peaks at the center and tapers off symmetrically on both sides, illustrating the probability density function of a normal distribution. - **Highlighted Area**: A portion of the graph is shaded in light green from the left side (around x = -4) to approximately x = 1.5. This shaded region represents the probability or proportion of data falling between these x-values. ### Educational Insights: - The highest point of the curve represents the mean of the data. - The shaded area could be used to show the probability of a random variable falling within a certain range, often used to calculate z-scores or critical values. - Understanding how to interpret this graph is essential in fields like statistics, research, and data analysis. This visual tool is valuable for those studying statistical methods and probability theory.
**PLOT-B Explanation** The text shows an R script used for plotting a statistical function: 1. **Define the Sequence for x-values:** ```R x <- seq(-4, 8, 0.01) ``` - This line creates a sequence from -4 to 8 with increments of 0.01, storing it in `x`. 2. **Calculate the y-values Using the Normal Distribution:** ```R y <- dnorm(x, 2.2, 1.9) ``` - This line calculates the density of the normal distribution for each value in `x` with a mean of 2.2 and a standard deviation of 1.9, storing it in `y`. 3. **Plot the Graph:** ```R plot(x, y, type = "l") ``` - This line plots the `x` and `y` values, producing a line graph (indicated by `type = "l"`). 4. **Highlight an Area Under the Curve:** ```R polygon(c(x[x < 1], 1), c(y[x < 1], y[x == -4]), col = "honeydew2") ``` - This line draws a polygon to highlight the area under the curve where `x` is less than 1. The color of the highlighted area is "honeydew2". **Graph Explanation:** - The graph represents a normal distribution curve with specific parameters. - It highlights the area under the curve from where `x` starts at -4, up to `x = 1`, with the specified color "honeydew2". This can be useful for statistical analysis or probability calculations.
Transcribed Image Text:**PLOT-B Explanation** The text shows an R script used for plotting a statistical function: 1. **Define the Sequence for x-values:** ```R x <- seq(-4, 8, 0.01) ``` - This line creates a sequence from -4 to 8 with increments of 0.01, storing it in `x`. 2. **Calculate the y-values Using the Normal Distribution:** ```R y <- dnorm(x, 2.2, 1.9) ``` - This line calculates the density of the normal distribution for each value in `x` with a mean of 2.2 and a standard deviation of 1.9, storing it in `y`. 3. **Plot the Graph:** ```R plot(x, y, type = "l") ``` - This line plots the `x` and `y` values, producing a line graph (indicated by `type = "l"`). 4. **Highlight an Area Under the Curve:** ```R polygon(c(x[x < 1], 1), c(y[x < 1], y[x == -4]), col = "honeydew2") ``` - This line draws a polygon to highlight the area under the curve where `x` is less than 1. The color of the highlighted area is "honeydew2". **Graph Explanation:** - The graph represents a normal distribution curve with specific parameters. - It highlights the area under the curve from where `x` starts at -4, up to `x = 1`, with the specified color "honeydew2". This can be useful for statistical analysis or probability calculations.
Expert Solution
Step 1:-

From the above code, 

x<seq(-4,8,0.01)

We see that the limits of x are -4 to 8. 
That means, -4<x<8 

y<dnorm(x,2.2,1.9)

We know that, 

y<dnorm(x,mean,standard deviation) 

So , mean = 2.2 and standard deviation = 1.9 

 

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