Using R, plot the exponential density function with param. A = 0.4 on interval ( − 1, 12).
Using R, plot the exponential density function with param. A = 0.4 on interval ( − 1, 12).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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.

Transcribed Image Text: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.

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.
Expert Solution
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