## Read data

x0<-c(1, 3, 5, 6)
x0

x1<-c(rep(x0, 2))
x1

x<-c(rep(1, 3), rep(2, 4))
x

m<-matrix(6, 3, 2 )
m

m<-matrix(x1, 4, 2)
m

m<-matrix(x1, 2, 4)
m

table<-read.table("file.dat", header=Ture )

# sample from a finite population: roll a die or toss a coin

x0<-c(1:6)                          # coin c(0, 1)
x0
sizen<-5                                  
x<-sample(x0, sizen)                # sample size is 5.
x

## Create random data from Normal population N(5, 1)

x.norm <- rnorm(n=100, m=5, sd=1)            
summary(x.norm)

par(mfrow=c(2,2))                              ## Graphics display: two by two 

hist(x.norm, main="Histogram")                 ## Histogram

boxplot(x.norm, main="Boxplot")                # Boxplot 

qqnorm(x.norm)                                 # QQ plot          
abline(mean(x.norm), sd(x.norm) )              # Add a straight line: y = a + b*x

z.norm <- (x.norm - mean(x.norm))/sd(x.norm)   # standardization

qqnorm(z.norm)                                 ## QQ-plot of z.norm
abline(0, 1)            



## Example 5.2.4, order statistics

x<-c(56, 70, 89, 94, 96, 101, rep(102, 3), 
     105, 106, 108, 110, 113, 116)
x
summary(x)                                    # five number summary and mean

par(mfrow=c(2,2))

hist(x, main="Histogram of the data")     

boxplot(x, main="Boxplot")      

qqnorm(x)

x.st<- (x- mean(x))/sd(x)  
qqnorm(x.st)          
abline(0, 1)           


# Define a function

F<-function(x)
{ x^2+x+3 }
F(5)

par(mfrow=c(2,2))

n=10
S=100

x<-mean(rnorm(n, 0, 1))                        # runif(n), rchisq(n, df), rt(n, df)
for (i in 1:(S-1))
  {  xbar<-mean(rnorm(n), 0, 1)
     x<-c(x, xbar)
     i=i+1 
 }
   hist(x, main="hist of xbar")
   boxplot(x, main="boxplot of xbar")
   qqnorm(x)
   abline(mean(x), sd(x))


n<-30
mu<-5
sigma<-1
alpha<-0.05
S<-1000

x<-rnorm(n, mu, sigma)                   # a sample from N(mu, sigma)

z<-qnorm(1-alpha/2, 0, 1)                # critical value  

CI.lower<-mean(x)-z*sigma/sqrt(n)        # lower limit of confidence interval
CI.upper<-mean(x)+z*sigma/sqrt(n)        # upper limit of confidence interval

v=(CI.lower<mu)&(CI.upper>mu)            # if true mu is between the uppper and lower limits
v
sum(v)


**************************************************************

Learning R in 15 minutes:

http://www.math.uic.edu/~jyang06/stat401/handouts/handout3.pdf