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x <-seq(-4,8,0.01) y <-dnorm(x, 2.2, 1.9) plot(x,y,type = "1") polygon(c(x[x>0], 0),c(y[x>0],y[x = = -4]),col = "honeydew2")

x <-seq(-4,8,0.01) y <-dnorm(x, 2.2, 1.9) plot(x,y,type = "1") polygon(c(x[x>0], 0),c(y[x>0],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) to 
express the  areas under the curves in terms of F(x). ( Do not calculate those areas. The 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 a

The image depicts a normal distribution curve with a shaded area under the curve. The graph is a standard normal distribution, which is symmetrical and bell-shaped, and represents a probability density function. - **Axes and Scale**: - The horizontal axis (x-axis) ranges from -4 to 8. This axis represents the variable for which the normal distribution is plotted. - The vertical axis (y-axis) ranges from 0.00 to 0.20 and represents the probability density. - **Curve**: - The curve follows the characteristic bell shape of a normal distribution, peaking at the mean. - **Shaded Area**: - The shaded area under the curve extends from approximately 0 to 3 on the x-axis. The shading likely represents the probability or proportion of the data that falls between these values. The total area under the normal distribution curve sums to 1, indicating probabilities across the distribution. This graph is useful in statistics for understanding how data is distributed around the mean and for calculating probabilities for continuous random variables within a specified range.
Transcribed Image Text:The image depicts a normal distribution curve with a shaded area under the curve. The graph is a standard normal distribution, which is symmetrical and bell-shaped, and represents a probability density function. - **Axes and Scale**: - The horizontal axis (x-axis) ranges from -4 to 8. This axis represents the variable for which the normal distribution is plotted. - The vertical axis (y-axis) ranges from 0.00 to 0.20 and represents the probability density. - **Curve**: - The curve follows the characteristic bell shape of a normal distribution, peaking at the mean. - **Shaded Area**: - The shaded area under the curve extends from approximately 0 to 3 on the x-axis. The shading likely represents the probability or proportion of the data that falls between these values. The total area under the normal distribution curve sums to 1, indicating probabilities across the distribution. This graph is useful in statistics for understanding how data is distributed around the mean and for calculating probabilities for continuous random variables within a specified range.
### PLOT-A The following R code generates a plot that visualizes a portion of a normal distribution curve and fills a specified area with color. ```r x <- seq(-4,8,0.01) # Creates a sequence of x values from -4 to 8 in increments of 0.01 y <- -dnorm(x,2.2,1.9) # Computes the negative density of a normal distribution with mean 2.2 and standard deviation 1.9 plot(x,y,type = "l") # Plots y against x as a line graph polygon( # Draws a polygon to highlight a specific area under the curve c(x[x > 0],0), # X coordinates: values where x is greater than 0, ending at 0 c(y[x > 0],y[x == -4]), # Y coordinates: corresponding y values for x > 0, ending at y value when x = -4 col = "honeydew2" # Fills the polygon with the color "honeydew2" ) ``` #### Explanation of the plot: - **X-axis:** Represents the values from -4 to 8. - **Y-axis:** Corresponds to the negative normal distribution values calculated for each x. - **Curve:** Illustrates the shape of the normal distribution, inverted due to the negative sign. - **Filled Area:** The polygon function shades the area for x > 0 up to x = -4, using the color "honeydew2" to visually distinguish this part of the distribution. This visualization can be useful for emphasizing specific sections of a probability distribution, such as the tail of the distribution beyond a certain point.
Transcribed Image Text:### PLOT-A The following R code generates a plot that visualizes a portion of a normal distribution curve and fills a specified area with color. ```r x <- seq(-4,8,0.01) # Creates a sequence of x values from -4 to 8 in increments of 0.01 y <- -dnorm(x,2.2,1.9) # Computes the negative density of a normal distribution with mean 2.2 and standard deviation 1.9 plot(x,y,type = "l") # Plots y against x as a line graph polygon( # Draws a polygon to highlight a specific area under the curve c(x[x > 0],0), # X coordinates: values where x is greater than 0, ending at 0 c(y[x > 0],y[x == -4]), # Y coordinates: corresponding y values for x > 0, ending at y value when x = -4 col = "honeydew2" # Fills the polygon with the color "honeydew2" ) ``` #### Explanation of the plot: - **X-axis:** Represents the values from -4 to 8. - **Y-axis:** Corresponds to the negative normal distribution values calculated for each x. - **Curve:** Illustrates the shape of the normal distribution, inverted due to the negative sign. - **Filled Area:** The polygon function shades the area for x > 0 up to x = -4, using the color "honeydew2" to visually distinguish this part of the distribution. This visualization can be useful for emphasizing specific sections of a probability distribution, such as the tail of the distribution beyond a certain point.
Expert Solution
Step 1:-

From the first line of the code we can see that, 

x<- seq(-4,8,0.01) 

The lower limit of x is -4 and upper limit is 8. 
The value of x is between- and 8. 
From the second line, 

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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