f. The expected losses.
The probability of making a certain observation h, fa or fa depends
of course on the state of nature, i.e. on the presence or absence of
a gross error.
e2 q
8 10 12
0
8
12
In fig. i, the situation has been sketched for the cases t o
and +io cm. The different possibilities can be visualized by
considering the areas under different parts of the curves. For
simplicity we can neglect some extremely small left tail regions
for 6i, and find in a table of the normal distribution the following
probabilities
Under 0i we have:
P{ <8}
P{8 12}
P{l2
Under 02 we have
P{ 8}
P{8 12}
P{I2
O.3085
O.383O
O.3085.
0.9545
O.O428
O.OO27.
127
Si
S2
S3
54
^5
*6
s7
s8
tl
«1
di
dl
a-2
d2
d2
d2
tl
di
di
d 2
d2
di
dl
d2
d2
tz
ai
d2
d2
dl
di
d2
d2
dl
TABLE 2.
Possible strategies
Figure i.
