Biomedical Engineering Reference
In-Depth Information
6.
In the example in Section 11.3 with
N
= 10
, the probabilities
P
3
,
P
6
,and
P
0
were evaluated.
(a)
Calculate the other values of
P
n
and show explicitly that the
P
n
add to give unity.
(b)
Plot the distribution
P
n
vs.
n
.
A sample consists of 16 atoms of
222
Rn.
(a)
7.
What is the probability that exactly one-half of the atoms
will decay in 2 d?
(b)
In 3 d?
(c)
Calculate the probability that one week could pass without
the decay of a single atom.
(d)
What is the probability that all of the atoms will decay in
the first day?
8.
(a)
In the last problem, what is the mean number of atoms
that decay in 2 d?
(b)
What is the mean value of the square of the number of
atoms that decay in 2 d?
(c)
What is the standard deviation of the number of atoms that
decay in 2 d?
Identical samples containing
32
P are measured for a period of
1 h in a counter, having an efficiency of 44% and negligible
background. From a large number of observations, the mean
number of counts in 1 h is found to be
2.92
9.
10
4
.
×
What is the activity of
32
Pinasample?
(a)
(b)
Estimate the standard deviation of the number of counts
obtained in 1 h.
Estimate the number of
32
P atoms in a sample in the last
problem.
10.
(a)
(b)
Estimate the standard deviation of the sample activity in Bq.
(c)
If the counter efficiency were 100% and the same mean
number of counts were observed in 1 h, what would be the
standard deviation of the activity in Bq?
11.
For the Poisson distribution, show that
P
n
+1
=
µP
n
/(
n
+1)
.
12.
For the Poisson distribution with
µ
=
4.0
, show that
0.195; and with
µ
=
8.0, show that
P
7
=
0.140.
P
3
=
P
4
=
P
8
=
13.
When the mean value
µ
of the Poisson distribution is an
integer, show that the probability of observing one less than the
mean is equal to the probability of observing the mean (as
illustrated by the last problem).
14.
Using a counter having an efficiency of 38% and negligible
background, a technician records a total of 1812 counts from a
long-lived radioactive source in 2 min.
(a)
Estimate the activity of the source in Bq.
(b)
Estimate the standard deviation of the activity.
