# binomial to normal
###################################################################
m=200;p=0.5;n=5
par(mfrow=c(1,3))
n=15
n=25
res=rbinom(m,n,p)
hist(res,prob=T,main="n=5")
curve(dnorm(x,n*p,sqrt(n*p*(1-p))),add=T)
qqnorm(res)

n=25
res=rbinom(m,n,p)
hist(res,main="n=5")
curve(dnorm(x,n*p,sqrt(n*p*(1-p))),add=T)
###################################################################
#xbar dis normal
###########################
res=c()
for (i in 1:100){
res[i]=mean(runif(10))}
qqnorm(res)
#########################
plot(0,0,type="n",xlim=c(0,1),ylim=c(0,13.5),xlab="Density estimate",ylab="f(x)")
m=500
a=0
b=1
n=c(2,10)#,25,100)
for (j in 1:2){
for (i in 1:m){res[i]=mean(runif(n[j],a,b))}

lines(density(res),lwd=2)  }
###########################################
# sample median
#x1,x2,.. from exponential(1) mean=1, median=log(2)=0.6931

f=function(n) median(rexp(n))
res25=c();res100=c();res400=c()
for (i in 1:m) res25[i]=f(25)
for (i in 1:m) res100[i]=f(100)
for (i in 1:m) res400[i]=f(400)

summary(res25)
summary(res100)
summary(res400)

plot(density(res400),xlim=range(res25),type="l",main="",xlab="Sampling distribution of median for n=25, 100, 400")
lines(density(res100))
lines(density(res25))

##############################
#geometric dist  mean=1/p for any p in [0,1]
#p(1-p)^(k-1)
firstSuccess=function(p){
k=0
success=FALSE
while(success==FALSE)
{
k=k+1
if(rbinom(1,1,p)==1) success=TRUE}
k}
m=500
res.5=c();res0.05=c()
for (i in 1:m) {res.5[i]=firstSuccess(0.5)
 res0.05[i]=firstSuccess(0.05)}
summary(res.5)
summary(res0.05)