Analyze The Sample Mean And Compare It To The Theoretical Mean

#console to analyze the sample mean and compare it to the theoretical mean
set.seed(1)
lambda<-0.2
nexp<-40
nsim<-1000
mns<-NULL
for(i in 1:nsim) mns<-c(mns,mean(rexp(40,lambda)))
hist(mns, col="blue", main="distributions of means of rexp")
## console for comparing the variance of the means vs the theoretical variance
varexp<-((1/lambda)^2)/nexp ##theoritical variance
varmean<-var(mns) ## variance of the means
##simulation initialization
lambda<-0.2
mu<-1/lambda
n<-40
nosim<-100
nosim2<-2000
simulations<-rexp(n*nosim2,lambda)
simulations40<-matrix(simulations[1:(n*nosim)],nosim)
simulations40by2000<-matrix(simulations,nosim2)
##comparing sample mean and theoritical mean
means<-cumsum(simulations[1:1000])/(1:1000)
library(ggplot2)