x <- c (1,3,2,5)
x

y = c(5,4,7)

length(x)

length(y)

ls()


x+y

x = matrix ( data = c (1,2,3,4), nrow=2, ncol=2)

matrix ( c(1,2,3,4),2,2,byrow=TRUE)

sqrt( x )


x = rnorm(50)
y = x + rnorm(50,mean=50,sd=.1)
cor(x,y)


set.seed(1303)
rnorm(50)

set.seed(3)
y = rnorm(100)
mean(y)

var(y)
sqrt(var(y))
sd (y)


x = rnorm(100)
y = rnorm(100)
plot(x,y)


pdf("Figure.pdf")
plot(x,y,col="green")
dev.off()

x = seq (1 ,10)
x =1:10
x = seq ( - pi , pi , length =50)


y=x
f = outer(x,y,function(x,y) cos(y)/(1+x^2))
contour(x,y,f)
contour(x,y,f,nlevels=45,add=T)
fa=(f-t(f))/2
contour(x,y,fa,nlevels=15)

image (x ,y , fa )
persp (x ,y , fa )
persp (x ,y , fa , theta =30)
persp (x ,y , fa , theta =30 , phi =20)
persp (x ,y , fa , theta =30 , phi =70)
persp (x ,y , fa , theta =30 , phi =40)