### Stat 3601

# generate a uniform(0,1) pseudo-random number

help(runif)		# get help on random uniform command

u <- runif(1)		# generate a single random uniform value

u			# prints u

# generate N = 1000 uniform(0,1) pseudo-random number and plot

N <- 1000		# number of interation	

u <- runif(N)		# create a vector of N uniforms

plot(u)			# plots the random uniforms

plot(u, type = "l")	# plots connecting the lines

# flip a fair coin 1 time

p <- 0.50		# P(H) = 0.5

H <- 0			# counter for H

u <- runif(1)		# generate a single random uniform value 
u

if(u < p) H <- 1	# simulate 1 flip of a fair coin

H			# print the result, 0 is T and 1 is H

# flip a fair coin N times

N <- 1000

p <- 0.50

H <- 0

for(i in 1:N){
	u <- runif(1)
	if(u < p) H <- H + 1
}

H

p.hat <- H/N		# estimated probability of H
p.hat

# make a plot that shows the relative frequency interpretation 
# of probability

N <- 1000		# number of flips

p <- 0.50		# probability of H

u <- runif(N)		# create a vector of N uniforms

H <- numeric(N)		# create a vector of N 0's

for(i in 1:N){		# simulate flipping the coin	
	if(u[i] < p) H[i] <- 1		
}

H.cumsum <- cumsum(H)	# sum up the number of H
#H.cumsum

p.hat <- numeric(N)

for(i in 1:N){
	p.hat[i] <- H.cumsum[i]/i	
}

p.hat

plot(p.hat, type = "l")

# roll a fair die 1 time

u <- runif(1)
u

D <- trunc(6*u) + 1
D

# roll a fair die N times and estimate P(3)

N <- 1000

u <- runif(N)

D <- trunc(6*u) + 1

br <- c(0.5,1.5,2.5,3.5,4.5,5.5,6.5)

hist(D, breaks = br)

Count <- 0
for(i in 1:N){
	if(D[i] == 3) Count <- Count + 1
}
Count/N

# roll a pair of fair dice N times

N <- 1000

u1 <- runif(N)

D1 <- trunc(6*u1) + 1

u2 <- runif(N)

D2 <- trunc(6*u2) + 1

D <- D1 + D2

br <- seq(0,12) + 0.5

hist(D, breaks = br)