R Notebook

mydata = matrix(c(1:6, c(10,15,19,26,32,37), c(11,16,17,28,35,39)),6,3)
mydata

##      [,1] [,2] [,3]
## [1,]    1   10   11
## [2,]    2   15   16
## [3,]    3   19   17
## [4,]    4   26   28
## [5,]    5   32   35
## [6,]    6   37   39

plot(mydata[,1], mydata[,2], type = "l", lwd = 8, xlim = c(01,10), ylim = c(0,40))

x1 = seq(-2,2,0.5)
x1

## [1] -2.0 -1.5 -1.0 -0.5  0.0  0.5  1.0  1.5  2.0

y1 = x1^3 - 3*x1
y1

## [1] -2.000  1.125  2.000  1.375  0.000 -1.375 -2.000 -1.125  2.000

x2 = seq(-2,2,0.01)
y2 = x2^3 - 3*x2
plot(x1,y1,type = "l")
lines(x2,y2,col = "red")

x = rnorm(100)
xgrid = seq(-4,4,0.1)
y = dnorm(xgrid)
hist(x,freq = F)
lines(xgrid,y,col="red")
points(xgrid,y,pch=3)

hist(x)

x = seq(-4,4,0.1) # A fine grid between (-4,4)
y = dnorm(x,0,1)
plot(x,y,type = "l")
lines(x,y,col = "red")
points(x,y,pch = 3)

par(mfrow = c(1,2))
plot(xgrid,y)
plot(xgrid,y,type = "l")

par(mfrow = c(2,1))
plot(xgrid,y)
plot(xgrid,y,type = "l")

x1 = seq(-3,3,0.01)
y1 = dnorm(x1)
x2 = seq(-4,4,0.1)
y2 = dnorm(x2)

par(mfrow=c(2,1))
plot(x1,y1,type = "l",col = "red")
plot(x2,y2,type = "l",col = "blue")

y = function(x) {
  y = x^2 + 2*x - 3
  return(y)
}
y(4)

## [1] 21

y(453)

## [1] 206112

a = function(z) {
  a = z^3 + 3*z - 3
  return(a)
}
a(4)

## [1] 73

a(453)

## [1] 92961033

y = function(x) {
  y = x^2 + 2*x - 3
  return(y)
}
a = function(z) {
  a = z^3 + 3*z - 3
  return(a)
}
par(mfrow = c(a,y))

## [[1]]
## NULL
## 
## [[2]]
## NULL

fx = function(x) {
  f = x^2 + 2*x - 3
  return(f)
}
fx(4)

## [1] 21

fx(400)

## [1] 160797

dice = function(n) {
  rolls = sample(1:6, size = n, replace = T)
  y = sum(rolls)
  print(rolls)
  return(y)
}
dice(2)

## [1] 6 5

## [1] 11

dice(20)

##  [1] 4 2 3 5 1 4 2 4 4 1 6 2 5 6 3 2 4 2 1 1

## [1] 62

myabs = function(x) {
  if (x<0) {
    print("The input is negative")
    x = -x
  }
  else {print("The input is >=0")}
}
myabs(-5)

## [1] "The input is negative"

myabs(5)

## [1] "The input is >=0"

roll.num = c(1,2,3,10)
M = length(roll.num)
sum.rolls = rep(0,M)
for (i in 1:M) {
  n = roll.num[i]
  sum.rolls[i] = dice(n)
}

## [1] 1
## [1] 6 5
## [1] 5 3 6
##  [1] 4 5 2 4 5 6 6 1 4 1

for (i in 1:20) {
  print(i^3)
}

## [1] 1
## [1] 8
## [1] 27
## [1] 64
## [1] 125
## [1] 216
## [1] 343
## [1] 512
## [1] 729
## [1] 1000
## [1] 1331
## [1] 1728
## [1] 2197
## [1] 2744
## [1] 3375
## [1] 4096
## [1] 4913
## [1] 5832
## [1] 6859
## [1] 8000

x = seq(-6,6,0.1)
M = length(x) 
fx.output = rep(0,M) 
for (i in 1:M) {
    fx.output[i] = fx(x[i])
  }
plot(x,fx.output,type = "l")