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## Author: Joshua M. Tebbs
## Date: 23 July 2025
## Update: 29 July 2025
## STAT 509 course notes: R Code Chapter 3
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# Use the following command as necessary
par(mar=c(4,4.5,4,3.5)) # adjust plotting region to avoid cutting off vertical axis label 

# Figure 3.1
# Page 24
x = c(0,1,2,3,4,5)
prob = c(0.60,0.10,0.16,0.05,0.06,0.03)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,max(prob)),cex.lab=1.25,lwd=2)
abline(h=0)


# Figure 3.2
# Page 25
x = c(0,1,2,3,4,5)
prob = c(0.60,0.10,0.16,0.05,0.06,0.03)
# Left (PMF)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,max(prob)),cex.lab=1.25,lwd=2)
abline(h=0)
# Right (CDF)
cdf = c(0,cumsum(prob))
cdf.plot = stepfun(x,cdf,f=0)
plot.stepfun(cdf.plot,xlab="x",ylab=expression(F[X](x)),verticals=FALSE,do.points=TRUE,main="",pch=16,cex.lab=1.25)


# Figure 3.3
# Page 27
x = c(0,1,2,3,4,5)
prob = c(0.60,0.10,0.16,0.05,0.06,0.03)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,max(prob)),cex.lab=1.25,lwd=2)
abline(h=0)
points(x=0.96,y=0,pch=19,cex=1.5)


# Figure 3.4
# Page 29
x = c(0,1,2,3)
prob = c(0.2,0.3,0.3,0.2)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),xaxp=c(0,3,3),ylim=c(0,0.35),cex.lab=1.25,lwd=2)
abline(h=0)
points(x=1.5,y=0,pch=19,cex=1.5)


# Figure 3.5
# Page 32
# Left (PMF of X)
x = c(1,2,3,4,5)
prob = c(0.38,0.27,0.18,0.11,0.06)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,0.4),cex.lab=1.25,lwd=2)
abline(h=0)
points(x=2.2,y=0,pch=19,cex=1.5)
# Right (PMF of Y)
plot(2*x-1,prob,type="h",xlab="y",ylab=expression(p[Y](y)),xaxp=c(1,9,4),ylim=c(0,0.4),cex.lab=1.25,lwd=2)
abline(h=0)
points(x=3.4,y=0,pch=19,cex=1.5)


# Figure 3.6
# Page 35
x = c(0,1,2,3,4)
prob = dbinom(x,4,0.4)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),xaxp=c(0,4,4),ylim=c(0,0.4),cex.lab=1.25,lwd=2)
abline(h=0)
points(x=1.6,y=0,pch=19,cex=1.5)


# Figure 3.7
# Page 36
x = seq(0,30,1)
prob = dbinom(x,30,0.05)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,max(prob)),cex.lab=1.25,lwd=2)
abline(h=0)


# Figure 3.8
# Page 39
x = seq(1,30,1)
prob = dgeom(x-1,0.20)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,max(prob)),cex.lab=1.25,lwd=2)
abline(h=0)


# Figure 3.9
# Page 41
x = seq(1,40,1)
prob = dnbinom(x-2,2,0.25)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,max(prob)),cex.lab=1.25,lwd=2)
abline(h=0)


# Figure 3.10
# Page 43
x = seq(0,5,1)
prob = dhyper(x,10,90,5)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,max(prob)),cex.lab=1.25,lwd=2)
abline(h=0)
points(x=0.5,y=0,pch=19,cex=1.5)


# Figure 3.11
# Page 46
x = seq(0,10,1)
prob = dpois(x,1.5)
plot(x,prob,type="h",xlab="x",ylab=expression(p[X](x)),ylim=c(0,max(prob)),cex.lab=1.25,lwd=2)
abline(h=0)
points(x=1.5,y=0,pch=19,cex=1.5)