onsider a machine that makes unfair coins. A coin that comes out of the
machine has probability
of head when tossed. The
itself is a random variable sampled from uniform distribution (on [0,1]). We
have some coin with unknown
.
We toss the coin and obtain head. What is the distribution of the result of
the next toss of the same coin?
Let
denote
(head) at
th
toss. We are interested in
.
We introduce a uniform mesh
on
and calculate using the formula (
Bayes
formula
):
According to the formula (
Total probability
rule
),
Hence,
