### This script plots the binomial probability mass function four

### times with different parameter values on the same scales.

 

### Plot the Binomial

 

x.max <- 50

 

par(mfrow=c(2,2))

 

# plot 1

 

n <- 20

p <- 0.5

 

x <- seq(0,x.max)

y <- dbinom(x,n,p)

plot(x,y,type='h', main="Bin(20,0.5)")

 

# plot 2

 

n <- 20

p <- 0.75

 

x <- seq(0,x.max)

y <- dbinom(x,n,p)

plot(x,y,type='h', main="Bin(20,0.75)")

 

# plot 3

 

n <- 40

p <- 0.75

 

x <- seq(0,x.max)

y <- dbinom(x,n,p)

plot(x,y,type='h', main="Bin(40,0.75)")

 

### Plot the Exponential

 

y.max <- 2

 

par(mfrow=c(2,2))

 

# plot 4

 

lambda <- 0.5    # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,10,0.01)

y <- dexp(x,lambda)

 

plot(x,y,type='l', main="Exp(0.5)", ylim=c(0,y.max))

 

# plot 5

 

lambda <- 1

 

x <- seq(0.01,10,0.01)

y <- dexp(x,lambda)

 

plot(x,y,type='l', main="Exp(1)", ylim=c(0,y.max))

 

# plot 6

 

lambda <- 2

 

x <- seq(0.01,10,0.01)

y <- dexp(x,lambda)

 

plot(x,y,type='l', main="Exp(2)", ylim=c(0,y.max))

 

### Plot the Gamma

 

y.max <- 3

 

par(mfrow=c(2,2))

 

# plot 7

 

alpha <- 0.5     # shape parameter

lambda <- 1      # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,20,0.01)

y <- dgamma(x,alpha,lambda)

 

plot(x,y,type='l', main="Gamma(0.5,1)", ylim=c(0,y.max))

 

# plot 8

 

alpha <- 1    # shape parameter

lambda <- 1      # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,20,0.01)

y <- dgamma(x,alpha,lambda)

 

plot(x,y,type='l', main="Gamma(1,1)", ylim=c(0,y.max))

 

y.max <- 0.3

 

# plot 9

 

alpha <- 5       # shape parameter

lambda <- 1      # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,20,0.01)

y <- dgamma(x,alpha,lambda)

 

plot(x,y,type='l', main="Gamma(5,1)", ylim=c(0,y.max))

 

# plot 10

 

alpha <- 10      # shape parameter

lambda <- 1      # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,20,0.01)

y <- dgamma(x,alpha,lambda)

 

plot(x,y,type='l', main="Gamma(5,1)", ylim=c(0,y.max))

 

y.max <- 2

 

par(mfrow=c(2,2))

 

# plot 11

 

alpha <- 2       # shape parameter

lambda <- 0.5    # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,10,0.01)

y <- dgamma(x,alpha,lambda)

 

plot(x,y,type='l', main="Gamma(2,0.5)", ylim=c(0,y.max))

 

# plot 12

 

alpha <- 2       # shape parameter

lambda <- 1      # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,10,0.01)

y <- dgamma(x,alpha,lambda)

 

plot(x,y,type='l', main="Gamma(2,1)", ylim=c(0,y.max))

 

# plot 13

 

alpha <- 2    # shape parameter

lambda <- 2      # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,10,0.01)

y <- dgamma(x,alpha,lambda)

 

plot(x,y,type='l', main="Gamma(2,2)", ylim=c(0,y.max))

 

# plot 14

 

alpha <- 2       # shape parameter

lambda <- 3      # note that this is the rate paramter = 1/scale paramter

 

x <- seq(0.01,10,0.01)

y <- dgamma(x,alpha,lambda)

 

plot(x,y,type='l', main="Gamma(2,3)", ylim=c(0,y.max))