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
![$\left[ 0,1\right] $](graphics/notesCF__0__408.gif)
and calculate using the formula (
Bayes
formula
):
According to the formula (
Total probability
rule
),
Hence,
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