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## Author: Joshua M. Tebbs
## Date: 23 December 2018
## Update: 1 January 2019
## STAT 512 course notes: R Code
## Chapter 7
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# Figure 7.1
# Page 56
t = seq(-5,5,0.01)
plot(t,dnorm(t,0,1),type="l",lty=1,xlab="",ylab="PDF",cex.lab=1.25)
lines(t,dt(t,3),lty=4)
lines(t,dt(t,10),lty=8)
abline(h=0)
legend(2,0.35,lty=c(1,4,8),c(expression(paste("N(0,1)")),expression(paste("t(3)")),expression(paste("t(10)"))))


# Figure 7.2
# Page 60
u = seq(0,8,0.01)
plot(u,df(u,1,10),type="l",lty=1,xlab="",ylab="PDF",cex.lab=1.25,ylim=c(0,1))
lines(u,df(u,5,50),lty=4)
lines(u,df(u,10,100),lty=8)
abline(h=0)
legend(3.5,0.6,lty=c(1,4,8),c(expression(paste(nu[1]," = 1, ",nu[2]," = 10")),expression(paste(nu[1]," = 5, ",nu[2], " = 50")),expression(paste(nu[1]," = 10, ", nu[2]," = 100"))))


# Figure 7.3
# Page 63
# Left
y = seq(0,10,1)
prob = dpois(y,2)
plot(y,prob,type="h",xlab="y",ylab="PMF",ylim=c(0,max(prob)),cex.lab=1.25)
abline(h=0)
# Right
y = seq(400,600,1)
prob = dpois(y,500)
plot(y,prob,type="h",xlab="t",ylab="Sampling distribution",ylim=c(0,max(prob)),cex.lab=1.25)
abline(h=0)
lines(y,dnorm(y,500,sqrt(500)),lty=1,col="red")
points(x=c(475,550),y=c(0,0),pch=19,cex=1.5)


# Figure 7.4
# Page 64
y = seq(0,120,0.1)
pdf = dexp(y,1/20)
plot(y,pdf,type="l",xlab="y",ylab="PDF",cex.lab=1.25)
abline(h=0)
abline(v=0,lty=2)


# Figure 7.5
# Page 65
# Left
y = seq(0,50,0.01)
plot(y,dgamma(y,10,1/2),type="l",lty=1,xlab="Sample mean",ylab="Exact sampling distribution",cex.lab=1.25)
abline(h=0)
x = seq(30,50,0.1)
y = dgamma(x,10,1/2)
polygon(c(30,x,50),c(0,y,0),col="lightblue")
points(x=30,y=0,pch=19,cex=1.5)
# Right
y = seq(-10,50,0.01)
plot(y,dnorm(y,20,sqrt(40)),type="l",lty=1,xlab="Sample mean",ylab="Approximate sampling distribution",cex.lab=1.25)
abline(h=0)
x = seq(30,50,0.1)
y = dnorm(x,20,sqrt(40))
polygon(c(30,x,50),c(0,y,0),col="lightblue")
points(x=30,y=0,pch=19,cex=1.5)


# Figure 7.6
# Page 66
y = seq(0,1,0.001)
pdf = (3/2)*(1-y^2)
plot(y,pdf,type="l",xlab="y",ylab="PDF",xlim=c(0,1),cex.lab=1.25)
abline(h=0)
abline(v=0,lty=2)


# Figure 7.7
# Page 68
t = seq(10,30,0.01)
plot(t,dnorm(t,19.5,sqrt(3.0875)),type="l",lty=1,xlab="t",ylab="Approximate sampling distribution",cex.lab=1.25)
abline(h=0)
x = seq(22.5,30,0.1)
y = dnorm(x,19.5,sqrt(3.0875))
polygon(c(22.5,x,30),c(0,y,0),col="lightblue")
points(x=22.5,y=0,pch=19,cex=1.5)


# Figure 7.8
# Page 72
# Left
t = seq(25,75,1)
prob = dbinom(t,100,0.5)
plot(t,prob,type="h",xlab="t",ylab="Sampling distribution",ylim=c(0,max(prob)),cex.lab=1.25)
abline(h=0)
t = seq(25,75,0.01)
lines(t,dnorm(t,50,sqrt(25)),lty=1,col="red")
# Right
t = seq(0,15,1)
prob = dbinom(t,40,0.1)
plot(t,prob,type="h",xlab="t",ylab="Sampling distribution",ylim=c(0,max(prob)),cex.lab=1.25)
abline(h=0)
t = seq(0,15,0.01)
lines(t,dnorm(t,4,sqrt(3.6)),lty=1,col="red")