Cons i de r th e fau lt of l e n gth C and t h e strnctu r e (powe r p l a n t) r ep r ese nt e d in the fi gu r e below . A n eart h qua k e occu r s ra n d o m ly along t h e faul t. L et us cons i...

Cons
i
de
r


th
e


fau
lt


of


l
e
n
gth



C



and

t

h
e


strnctu
r
e


(powe
r


p
l
a
n
t)


r
ep
r
ese
nt
e
d


in


the


fi
gu
r
e


below
.


A
n


eart
h
qua
k
e


occu
r
s


ra
n
d
o
m
ly


along

t

h
e


faul
t.


L
et


us

cons

i
de
r


t
h
e


d
i
s
t
an
c
e



R



fro
m


t
h
e


stru
c
tu
r
e


to


th
e


ep
i
ce
n
ter


of

t

h
e


earth
q
uake

(i

.
e.
,


epicen
t
ra
l


d
i
stanc
e
)
.


Ass
u
me


t
h
at


th
e


epice
nter


i
s


eq
u
a
ll
y


likely
to


occur


anywhere
along
the


fa
ult


(from


one


e
n
d


to the


o
t
h
e
r


end
of


t
h
e


fa
ult
).

(a)



Derive

th

e


C
D
P


an
d

P

DF


(in


t
hat


order)


of


t
he


ep
i
ce
n
tral


d
istance



R



(ran
d
om


variab
l
e)


a
nd

a
p
p
l
y


the

res

ult
s


t
o


th
e


follow
in
g


s
p
e
cific


case
:

C



=
300


mi
,



d



=


2
0


mi

(b)



Pl

o
t


t
h
e

P

DF


a
n
d
CD

F


ofra

n
dom


va


1
i
ab

l
e


R.

(c)



What
is


th

e
probab

i
lity


t
hat


i
n
the


n
e
x
t


eaithq

u
ake


generated


by


t
h
i
s
fa

ult

,


th

e


e
p
icen
t
ra

l

d

is

t
ance



R



will
be less


t
h
a
n


or


eq
u
al


to


5
0


miles?