Gw mau tau Conto dari Téoréma Bayes. Jelasin dalam bahasa sunda

Suppose the proportion R of voters who will vote "yes" in a referendum is sebaran seragam between 0 and 1. That is the prior probability distribution of R. A random sample of 10 voters is taken, and it is found that seven of them will vote "yes". The conditional distribution of the number X of voters in this small sample who will vote "yes", given that (capital) R is some particular number (lower-case) r, is a sebaran binomial with paraméters 10 and r, i.e., it is the distribution of the number of "successes" in 10 independent Bernoulli trials with probability r of success on éach trial. One therefore has

Since X was observed to be 7, the likelihood function is

for 0 ≤ r ≤ 1. The prior probability density function is

and 0 otherwise. Multiplying the prior by the likelihood, we get

if 0 ≤ r ≤ 1, and 0 otherwise. Integrating, we get

so the posterior probability density function is

for r between 0 and 1, and 0 otherwise.

One may be interested in the probability that more than half the voters will vote "yes". The prior probability that more than half the voters will vote "yes" is 1/2, by the symmetry of the sebaran seragam. The posterior probability that more than half the voters will vote "yes", i.e., the conditional probability given the outcome of the opinion poll—that seven of the 10 voters questioned will vote "yes"—is