Geoscience Reference
In-Depth Information
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PROBLEMS
13.1
Prove both equations in (13.12).
13.2
Determine the second moment
m
2
=
σ
2
for the exponential distribution in terms of
λ
. The expo-
nential distribution has a density
f
(
x
)
=
λ
e
−
λ
x
for
x
≥
0 and
f
(
x
)
=
0 for
x
<
0.
13.3
Determine the fourth septile (i.e.
n
=
7) and the fifth octile (i.e.
n
=
8) for the exponential distri-
bution as defined in the previous problem.
13.4
Calculate the mean
μ
and the variance
σ
2
for the power distribution defined in Equations (13.85)
and (13.86) in terms of
a
and
b
.
13.5
Calculate the 95th percentile for the power distribution defined in Equations (13.85) and (13.86)
in terms of
a
and
b
.
