<s>
In	O
statistics	O
,	O
the	O
question	O
of	O
checking	B-General_Concept
whether	I-General_Concept
a	I-General_Concept
coin	I-General_Concept
is	I-General_Concept
fair	I-General_Concept
is	O
one	O
whose	O
importance	O
lies	O
,	O
firstly	O
,	O
in	O
providing	O
a	O
simple	O
problem	O
on	O
which	O
to	O
illustrate	O
basic	O
ideas	O
of	O
statistical	O
inference	O
and	O
,	O
secondly	O
,	O
in	O
providing	O
a	O
simple	O
problem	O
that	O
can	O
be	O
used	O
to	O
compare	O
various	O
competing	O
methods	O
of	O
statistical	O
inference	O
,	O
including	O
decision	O
theory	O
.	O
</s>
<s>
The	O
practical	O
problem	O
of	O
checking	B-General_Concept
whether	I-General_Concept
a	I-General_Concept
coin	I-General_Concept
is	I-General_Concept
fair	I-General_Concept
might	O
be	O
considered	O
as	O
easily	O
solved	O
by	O
performing	O
a	O
sufficiently	O
large	O
number	O
of	O
trials	O
,	O
but	O
statistics	O
and	O
probability	O
theory	O
can	O
provide	O
guidance	O
on	O
two	O
types	O
of	O
question	O
;	O
specifically	O
those	O
of	O
how	O
many	O
trials	O
to	O
undertake	O
and	O
of	O
the	O
accuracy	O
of	O
an	O
estimate	O
of	O
the	O
probability	O
of	O
turning	O
up	O
heads	O
,	O
derived	O
from	O
a	O
given	O
sample	O
of	O
trials	O
.	O
</s>
<s>
Estimator	B-General_Concept
of	I-General_Concept
true	I-General_Concept
probability	I-General_Concept
(	O
Frequentist	O
approach	O
)	O
.	O
</s>
<s>
In	O
statistics	O
,	O
the	O
estimate	O
of	O
a	O
proportion	O
of	O
a	O
sample	O
(	O
denoted	O
by	O
p	O
)	O
has	O
a	O
standard	B-General_Concept
error	I-General_Concept
given	O
by	O
:	O
</s>
<s>
This	O
standard	B-General_Concept
error	I-General_Concept
function	O
of	O
p	O
has	O
a	O
maximum	O
at	O
.	O
</s>
<s>
Other	O
approaches	O
to	O
the	O
question	O
of	O
checking	B-General_Concept
whether	I-General_Concept
a	I-General_Concept
coin	I-General_Concept
is	I-General_Concept
fair	I-General_Concept
are	O
available	O
using	O
decision	O
theory	O
,	O
whose	O
application	O
would	O
require	O
the	O
formulation	O
of	O
a	O
loss	O
function	O
or	O
utility	O
function	O
which	O
describes	O
the	O
consequences	O
of	O
making	O
a	O
given	O
decision	O
.	O
</s>
