setwd("~/Data/Statistical Inference Coure Project")
require(knitr)
## Loading required package: knitr
require(ggplot2)
## Loading required package: ggplot2
opts_chunk$set(echo=TRUE)
set.seed(1)
n<-40
lambda<-0.2
numsim<-2000
dataset<-matrix(rexp(n*numsim,lambda),numsim)
TheoryMean<-1/lambda
RowMeans<-apply(dataset,1,mean)
ActualMean<-mean(RowMeans)
TheorySD<-((1/lambda) * (1/sqrt(n)))
ActualSD<-sd(RowMeans)
TheoryVar<-TheorySD^2
ActualVar<-var(RowMeans)
dfRowMeans<-data.frame(RowMeans) # convert to data.frame for ggplot
mp<-ggplot(dfRowMeans,aes(x=RowMeans))
mp<-mp+geom_histogram(binwidth = lambda,fill="green",color="black",aes(y = ..density..))
mp<-mp + labs(title="Density of 40 Numbers from Exponential Distribution", x="Mean of 40 Selections", y="Density")
mp<-mp + geom_vline(xintercept=ActualMean,size=1.0, color="black") # add a line for the actual mean
mp<-mp + stat_function(fun=dnorm,args=list(mean=ActualMean, sd=ActualSD),color = "blue", size = 1.0)
mp<-mp + geom_vline(xintercept=TheoryMean,size=1.0,color="yellow",linetype = "longdash")
mp<-mp + stat_function(fun=dnorm,args=list(mean=TheoryMean, sd=TheorySD),color = "red", size = 1.0)
mp

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