set.seed(123)
require(latex2exp)

## Loading required package: latex2exp

t_given_H0 <- rbeta(1000,2,5)
t_given_H1 <- rnorm(1000,1,0.2)

plot(density(t_given_H1),xlim=c(-2,2),ylim=c(0,3),col="blue",xlab="t",ylab="g(t)",main=TeX("Illustration of Statistical Test Distributions: g(t|H_0) vs g(t|H_1)"))
lines(density(t_given_H0),col="red")
abline(v=0.63,col="black",lty="dotted",lwd=2)
text(x=0.76,y=2,TeX("t_{cut}"),cex=1.5)
arrows(x0=0.63,x1=0,9,y0=3,y1=3,length=0.4,lwd=1,code=2,col="red")
arrows(x0=0.63,x1=1.26,9,y0=3,y1=3,length=0.4,lwd=1,code=2,col="blue")

text(x=-0.2,y=2,TeX("g(t|H_0)"),col="red")
text(x=1.3,y=2,TeX("g(t|H_1)"),col="blue")
text(x=0.2,y=2.8,TeX("Accept H_0"))
text(x=1.2,y=2.8,TeX("Reject H_0"))