### Use of the Bolstad R library

# Bayesian inference for the Binomial p, one sample of size n,
# conjugate Beta prior

library(Bolstad)

help(binobp)  # beta prior

# binobp(x, n, a = 1, b = 1, ret = FALSE)

#######################################################################

n = 1  # draw one ball

x = 1  # one ball drawn that is a "success"

binobp(x,n, a=1, b=1)   # uniform prior on theta

#######################################################################

n = 2  # draw one balls

x = 1  # one ball drawn that is a "success"

binobp(x,n, a=1, b=1)   # uniform prior on theta

#######################################################################

n = 30  # draw one balls

x = 20  # one ball drawn that is a "success"

binobp(x,n, a=1, b=1)   # uniform prior on theta

#######################################################################

n = 300  # draw one balls

x = 200  # one ball drawn that is a "success"

binobp(x,n, a=1, b=1)   # uniform prior on theta

#######################################################################

n = 30  # draw one balls

x = 20  # one ball drawn that is a "success"

binobp(x,n, a=2, b=2)   # non-uniform prior on theta

#######################################################################

n = 300  # draw one balls

x = 200  # one ball drawn that is a "success"

binobp(x,n, a=2, b=4)   # non-uniform prior on theta