#Objective: HW1
#Author: Zhiwu
#Date: Jan 17,2018

#Define function for new variable
zhang=function(k,dfx,df1,df2){
	x2=rchisq(k,dfx)
	f=rf(k,df1,df2)
	y=x2+f
	return(y)
}

#Distribution of the variables
k=10000
myZhang=zhang(k,dfx=1,df1=1,df2=10)
plot(myZhang)
hist(myZhang)

#Define function for new statistics
ZhangStatistics=function(k,size=30,dfx=1,df1=1,df2=10){
rr=replicate(k,
{
s=zhang(size,dfx,df1,df2)
theMax=max(s)
theMin=min(s)
range=theMax-theMin
})
return(rr)
}

#Distribution of the statistics
myStatistics=ZhangStatistics(10000,size=200,dfx=1,df1=1,df2=10)
length(myStatistics)
plot(myStatistics)
hist(myStatistics)
plot(density(myStatistics))