# Beta distribution

x<-seq(from=0, to=1, by=.01)
# Beta(1,1)
plot(x,dbeta(x,1,1),col=1,type="l",xlim=c(0,1),ylim=c(0,4.5),ylab="Beta(a,b)") 
# Beta(5,2)
lines(x,dbeta(x,5,2),col=2)
# Beta(3,8)
lines(x,dbeta(x,3,8),col=3)
# Beta(2,10)
lines(x,dbeta(x,2,10),col=4)

# X ~ Beta(5,2)
# P(X > 0.7)
1-pbeta(0.7,5,2)
# P(0.2<X<0.5)
pbeta(0.5,5,2)-pbeta(0.2,5,2)
# value of X that corresponds to the 80th percentile
qbeta(0.8,5,2)