set.seed(12345)

n<-10000;

z1<-rnorm(n,0,1)
z2<-rnorm(n,0,1)
z3<-rnorm(n,0,1)
z4<-rnorm(n,0,1)
z5<-rnorm(n,0,1)

chi5<-z1^2+z2^2+z3^2+z4^2+z5^2
(mean(chi5))
(var(chi5))
hist(chi5,  freq=F, col="grey", xlab="", xlim=c(0, 25), breaks=100)

par(new=T)
plot(density(chi5), axes=F, main="", xlim=c(0, 25), lwd=2, col="blue")

df_list<-c(5,10,20,30)
par(mfrow=c(2,2))

for (i in 1:length(df_list)) {
  hist(rchisq(n, df=df_list[i], ncp=0), breaks=100, xlab="chisq", main=paste("df=", df_list[i]))
}

n_list<-c(2,5,7,9) # Ç¥º»¼ö(n)
df_list<-n_list-1 # ÀÚÀ¯µµ

par(mfrow=c(1,1))
curve(dchisq(x, 1, ncp=0), col="blue", xlim=c(0, 16), ylim=c(0, 0.8), xlab="chisq", ylab="f(chisq)")
curve(dchisq(x, 4, ncp=0), add=T, col="red", xlim=c(0, 16), ylim=c(0, 0.8), xlab="chisq", ylab="f(chisq)")
curve(dchisq(x, 6, ncp=0), add=T, col="green", xlim=c(0, 16), ylim=c(0, 0.8), xlab="chisq", ylab="f(chisq)")
curve(dchisq(x, 8, ncp=0), add=T, col="black", xlim=c(0, 16), ylim=c(0, 0.8), xlab="chisq", ylab="f(chisq)")

par(mfrow=c(2,2))
for (i in 1:length(df_list)) {
  curve(dchisq(x, df_list[i], ncp=0), add=F, xlim=c(0, 16), ylim=c(0, 0.8), xlab="chisq", ylab="f(chisq)", main=paste("df=", df_list[i])) }

df<-10

chi1<-numeric(df)
chi2<-numeric(df)
chi3<-numeric(df)
chi4<-numeric(df)
chi5<-numeric(df)
chi6<-numeric(df)

for(j in 1:df) {chi1[j]<-qchisq(0.01,j)}

for(j in 1:df) {chi2[j]<-qchisq(0.05,j)}

for(j in 1:df) {chi3[j]<-qchisq(0.1,j)}

for(j in 1:df) {chi4[j]<-qchisq(0.9,j)}

for(j in 1:df) {chi5[j]<-qchisq(0.95,j)}

for(j in 1:df) {chi6[j]<-qchisq(0.99,j)}

round((chi<-cbind(chi1,chi2,chi3,chi4,chi5, chi6)),digits=4)