## This is the hint program for game 5. 
# Essential the history dump from class R codes. Enjoy!
# by Kno Tsao
x<-runif(20)
summary(x)
plot(x) 
plot(x,dunif(x),main="pdf of U(0,1)")
plot(x,punif(x),main="cdf of U(0,1)")
# Reassign x
x<-seq(from=0,to=1,length.out=1000)

# Setup/Plots for U(0,1)
windows()
par(mfrow=c(2,2)); 
plot(x,dunif(x),main="pdf of U(0,1)") # Standardized histograms
x10<-runif(10,min=0,max=1);
x100<-runif(100,min=0,max=1);
x1000<-runif(1000,min=0,max=1);
hist(x10,main="10 samples from U(0,1)",prob=TRUE);
hist(x100,main="100 samples from U(0,1)",prob=TRUE);
hist(x1000,main="1000 samples from U(0,1)",prob=TRUE);

# Closer examination of the plot for 10 samples from U(0,1)
hist(x10,main="10 samples from U(0,1)");
x10<-sort(x10)
x10[0<= x10 & x10 <=0.2]
x10[0.6<= x10 & x10 <=0.8]
sum((0.6<= x10 & x10 <=0.8)*1) # no. of x10 lie between [0.6,0.8]

# Even larger sample sizes
windows()
par(mfrow=c(2,2)); 
x<-seq(from=0,to=1,length.out=1000)
plot(x,dunif(x),main="pdf of U(0,1)") 
xe3<-runif(10^3,min=0,max=1);
xe6<-runif(10^6,min=0,max=1);
xe7<-runif(10^7,min=0,max=1);
# Standardized histograms
hist(xe3,main="10^3 samples from U(0,1)",prob=TRUE);
hist(xe6,main="10^6 samples from U(0,1)",prob=TRUE);
hist(xe9,main="10^7 samples from U(0,1)",prob=TRUE);

# U(0,0.5)
windows()
par(mfrow=c(2,2)); 
x<-seq(from=0,to=1,length.out=1000)
plot(x,dunif(x,min=0,max=.5),main="pdf of U(0,.5)") # Standardized histograms
xe3<-runif(10^3,min=0,max=.5);
xe6<-runif(10^6,min=0,max=.5);
xe7<-runif(10^7,min=0,max=.5);
hist(xe3,main="10^3 samples from U(0,.5)",prob=TRUE);
hist(xe6,main="10^6 samples from U(0,.5)",prob=TRUE);
hist(xe7,main="10^7 samples from U(0,.5)",prob=TRUE);

# Discrete Uniform from stackexchange
# http://stats.stackexchange.com/questions/3930/are-there-default-functions-for-discrete-uniform-distributions-in-r
rdu<-function(n,k) sample(1:k,n,replace=T)
ddu<-function(x,k) ifelse(x>=1 & x<=k & round(x)==x,1/k,0) 
pdu<-function(x,k) ifelse(x<1,0,ifelse(x<=k,floor(x)/k,1))

# You may use these user-defined functions to construct similar plots/figures