Biomedical Engineering Reference
In-Depth Information
Fig. 11.2
Comparison of binomial (histogram) and Poisson
(solid bars) distributions for fixed
N
and different
p
.The
ordinate shows
P
n
and the abscissa,
n
. The mean of the two
distributions in a given panel is the same. (Courtesy James S.
Bogard.)
depends on the extent to which
p
1
and
N
1
. In the last two examples, involv-
ing 37 Bq of
42
K and 1-s counting intervals, the Poisson description was seen to
be extremely accurate. We had for the probability of success (decay)
p
=
10
-5
1.55
×
10
6
trials (atoms).
Figure 11.2 shows a comparison of another sort, in which
N
=
and
N
=
2.39
×
100
is held con-
stant and
p
is varied. The middle panel on the right (
p
=
0.10
)isthesameas
in Fig. 11.1. The mean value is the same for both distributions in each panel of
Fig. 11.2; but it shifts from panel to panel, becoming progressively smaller as
p
is
decreased. Again, we see that the binomial and Poisson distributions become vir-
