### 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))