Suppose that the exponential distribution would be used to fit the data. Use R to fit the parameters by the method of moments and maximum likelihood.

Sure, I can help you with that! To fit the exponential distribution to your data in R, you can use the `fitdistr` function from the `MASS` package. Here's an example of how to fit the distribution using both the method of moments and maximum likelihood:

# Load the MASS package
library(MASS)

# Generate some example data
set.seed(123)
data <- rexp(100, rate = 0.5)

# Fit the exponential distribution using the method of moments
mu <- mean(data)
lambda_mom <- 1 / mu
print(paste0("Method of moments estimate: ", lambda_mom))

# Fit the exponential distribution using maximum likelihood
fit_mle <- fitdistr(data, "exponential", method = "MLE")
lambda_mle <- fit_mle$estimate
print(paste0("Maximum likelihood estimate: ", lambda_mle))

In this example, we first generate some example data from an exponential distribution with a rate parameter of 0.5. We then use the method of moments to estimate the rate parameter by taking the reciprocal of the sample mean. Finally, we use maximum likelihood estimation to fit the distribution to the data using the `fitdistr` function. The `fitdistr` function takes three arguments: the data, the name of the distribution to fit ("exponential" in this case), and the method of estimation ("MLE" for maximum likelihood estimation). The resulting output gives us the maximum likelihood estimate of the rate parameter.