Answered: Using R, plot the exponential density…

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

Please provide a source code that can be copied and run into R - Programming.

The secomd image is an example of how the question's code should somewhat look.

Below is the plot of an exponential density function with parameter $\lambda = 0.5$.

```r
x <- seq(-4, 12, 0.01)
y <- dexp(x, 0.5)
plot(x, y, type = "l", col = "blue")
```

**Explanation:**

- The code snippet is used to generate a plot of the exponential density function.
- `seq(-4, 12, 0.01)` creates a sequence of x-values starting at -4 and ending at 12, with increments of 0.01.
- `dexp(x, 0.5)` calculates the exponential density function values for the x-values with a rate parameter ($\lambda$) of 0.5.
- `plot(x, y, type = "l", col = "blue")` creates a line plot of the exponential density function values (y) against the x-values, with the line colored blue.

The plot visually represents how the exponential density function behaves for the given parameter.

$**Title:** Plotting an Exponential Density Function in R **Objective:** Learn how to plot the exponential density function using R with a specified parameter and interval. **Task:** Using R, plot the exponential density function with parameter $ \lambda = 0.4 $ on the interval $ (-1, 12) $. **Steps:** 1. **Setup R Environment:** - Ensure you have R installed on your system. - Open RStudio or any R console for scripting. 2. **Define the Parameters:** - Set $ \lambda = 0.4 $ for the exponential distribution. 3. **Plotting the Function:** - Use R’s plotting functions (such as `curve` and `dexp`) to visualize the exponential density. - Ensure your x-values range from -1 to 12. 4. **Code Example:** ```R # Define the lambda parameter lambda <- 0.4 # Plot the exponential density function curve(dexp(x, rate=lambda), from=-1, to=12, col='blue', lwd=2, ylab='Density', xlab='x', main='Exponential Density Function') ``` 5. **Explanation of the Plot:** - The x-axis represents the range from -1 to 12. - The y-axis corresponds to the density values. - The exponential curve should start at zero (or close to zero for negative values) and depict a decreasing trend as x increases, showing the characteristic exponential decay. 6. **Discussion Points:** - Explore how changing $ \lambda $ affects the shape of the curve. - Discuss real-world applications of the exponential distribution, such as modeling time between events in a Poisson process. By following these steps, you can effectively plot and analyze exponential density functions using the R programming language.$

Transcribed Image Text:**Title:** Plotting an Exponential Density Function in R **Objective:** Learn how to plot the exponential density function using R with a specified parameter and interval. **Task:** Using R, plot the exponential density function with parameter $ \lambda = 0.4 $ on the interval $ (-1, 12) $. **Steps:** 1. **Setup R Environment:** - Ensure you have R installed on your system. - Open RStudio or any R console for scripting. 2. **Define the Parameters:** - Set $ \lambda = 0.4 $ for the exponential distribution. 3. **Plotting the Function:** - Use R’s plotting functions (such as `curve` and `dexp`) to visualize the exponential density. - Ensure your x-values range from -1 to 12. 4. **Code Example:** ```R # Define the lambda parameter lambda <- 0.4 # Plot the exponential density function curve(dexp(x, rate=lambda), from=-1, to=12, col='blue', lwd=2, ylab='Density', xlab='x', main='Exponential Density Function') ``` 5. **Explanation of the Plot:** - The x-axis represents the range from -1 to 12. - The y-axis corresponds to the density values. - The exponential curve should start at zero (or close to zero for negative values) and depict a decreasing trend as x increases, showing the characteristic exponential decay. 6. **Discussion Points:** - Explore how changing $ \lambda $ affects the shape of the curve. - Discuss real-world applications of the exponential distribution, such as modeling time between events in a Poisson process. By following these steps, you can effectively plot and analyze exponential density functions using the R programming language.

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