Basics..R

library(ggplot2)
vv=seq(5,20,length.out = 4)
r=seq(0,25,length.out = 500)
x=c()
for (v in vv) {
  nd=data.frame(x=r,density=dchisq(r,v),v)
  x=rbind(x,nd)
}
x=transform(x,v=factor(v))
ggplot(x)+
  geom_line(aes(x=x,y=density,lty=v))+
  labs(title="Behavior of Chi-squared Distribution of v")

y=dchisq(r,7) ; d=data.frame(x=r,density=y,
                             probability=ifelse(r>=qchisq(.95,7),"5%","95%"))
ggplot(d)+geom_line(aes(x=x,y=density))+labs(title="v=7")+
  geom_area(aes(x=x,y=density,fill=probability))

r=seq(-3,3,length.out = 300)
t=dt(r,2)
n=dnorm(r)
d=data.frame(r,density=t,dist="t (2)")
d=rbind(d,data.frame(r,density=n,dist="N (0,1)"))
ggplot(d)+geom_line(aes(x=r,y=density,lty=dist))

r=seq(0,5,length.out = 300)
f1=df(r,2,4)
f2=df(r,12,12)
f3=df(r,20,20)
f4=df(r,10,30)
d=data.frame(r,density=f1,dist="F (2,4)")
d=rbind(d,data.frame(r,density=f2,dist="F (12,12)"))
d=rbind(d,data.frame(r,density=f3,dist="F (20,20)"))
d=rbind(d,data.frame(r,density=f4,dist="F (10,30)"))
ggplot(d)+geom_line(aes(x=r,y=density,color=dist),lwd=1.1)