5. Use R to calculate and simulate with the exponential distribution as follows. (a) For an exponential random variable X with A = 4, simulate 1000 independent exponential random variables by using...

Solve in R programming language:

5) Use R to calculate and simulate with the exponential distribution as follows.

(a) For an exponential random variable X with λ = 4, simulate 1000 independent exponential random variables by using the R function rexp(n, λ). Calculate the mean and variance of this sample.

(b) Compare the empirical results from part (a) with the distribution mean 1/λ and the distribution standard deviation 1/λ.

Extracted text: 5. Use R to calculate and simulate with the exponential distribution as follows. (a) For an exponential random variable X with A = 4, simulate 1000 independent exponential random variables by using the R function rexp(n, A). Calculate the mean and variance of this sample. (b) Compare the empirical results from part (a) with the distribution mean 1/A and the distribution standard deviation 1/A.


Extracted text: 5. Use R to calculate and simulate with the exponential distribution as follows. (a) For an exponential random variable X with A = 4, simulate 1000 independent exponential random variables by using the R function rexp(n, A). Calculate the mean and variance of this sample. (b) Compare the empirical results from part (a) with the distribution mean 1/A and the distribution standard deviation 1/A.