Exponential Distribution and the Central Limit Theorem
Exponential Distribution and the Central Limit Theorem Bryan Cole
Overview
Saturday, November 21, 2015
In this project I will investigate properties of the distribution of the mean of 40 exponentials in R in order to demonstrate some properties of the Central Limit Theorem. To accomplish this, the three following tasks are performed via simulation and associated explanatory text: 1.Show the sample mean and compare it to the theoretical mean of the distribution.
2.Show how variable the sample is (via variance) and compare it to the theoretical variance of the distribution. 3.Show that the distribution is approximately normal (CLT).
Simulations
The exponential distribution can be simulated in R with rexp(n, lambda) where lambda is the rate parameter. The mean of exponential distribution is 1/lambda and the standard deviation is also 1/lambda. For these simulations, we set lambda to 0.2, n= 40 and investigate the distribution of averages in 1000 different simulations. # set seed for reproducibility of random number generation set.seed(10)
# perform 1000 simulations of the mean of the exponential dist. (n=40,lambda=0.2) mns
Overview
Saturday, November 21, 2015
In this project I will investigate properties of the distribution of the mean of 40 exponentials in R in order to demonstrate some properties of the Central Limit Theorem. To accomplish this, the three following tasks are performed via simulation and associated explanatory text: 1.Show the sample mean and compare it to the theoretical mean of the distribution.
2.Show how variable the sample is (via variance) and compare it to the theoretical variance of the distribution. 3.Show that the distribution is approximately normal (CLT).
Simulations
The exponential distribution can be simulated in R with rexp(n, lambda) where lambda is the rate parameter. The mean of exponential distribution is 1/lambda and the standard deviation is also 1/lambda. For these simulations, we set lambda to 0.2, n= 40 and investigate the distribution of averages in 1000 different simulations. # set seed for reproducibility of random number generation set.seed(10)
# perform 1000 simulations of the mean of the exponential dist. (n=40,lambda=0.2) mns
