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Problem 1. (20+10
=
30 points1
The radioactivity of a material at time
t
is given by the formula
R,
=
Ro exp(At)
where Ro is the radioactivity at time
t
=
0 and A is the rate of percent decay per unit
time. Suppose Ro and A are random variables with the second moments listed below:
a) For
t
=
10, using firstorder approximations, determine the mean and standard devia
tion of R, and the correlation coefficient between R, and A.
b) Determine the relative importance of the random variables Ro and
A
in contributing
to the variability of R,
.
Variable
R
o
A
a)
pR,
E
100
x
exp(0.05 x 10)
=
60.653
Ans.
Standard
deviation
3 0
0.02
Mean
100
0.05
o;
E
(0.607)'(30)'
+
(606.530)'(0.02)'
+
2(0.607)(606.530)(0.3)(30)(0.02)
=
331.091 +147.152132.437
=
345.806
oRl
=18.6
Ans.

0.133
PRfA
(18.6)(0.02)
=0.358
Ans.
Correlation coefficients
b)
Imp(R,)
=
10.6071 x 30
=
18.196, Imp(A)
=
1
606.5301 x 0.02
=
12.131
Imp(R,
)
>
Imp(A)
Ans.
R
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This note was uploaded on 07/11/2009 for the course CEE cee taught by Professor Monteiro during the Fall '05 term at University of California, Berkeley.
 Fall '05
 MONTEIRO

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