Consider the fault of length C and the strncture (power plant) represented in the figure below. An...

Question

Consider the fault of length C and the strncture (power plant) represented in the figure below. An earthquake occurs randomly along the fault. Let us consider the distance R from the structure to the epicenter of the earthquake (i.e., epicentral distance). Assume that the epicenter is equally likely to occur anywhere along the fault (from one end to the other end of the fault).

(a)
Derive the CDP and PDF (in that order) of the epicentral distance R (random variable) and apply the results to the following specific case:

C =300 mi, d = 20 mi

(b) Plot the PDF and CDF ofrandom va 1iable R.

(c)
What is the probability that in the next eaithquake generated by this fault, the epicentral distance R will be less than or equal to 50 miles?

In the next earthquake, if the shortest distance R is Jess than I 00 miles, what is the probability that it will be less than 50 miles? Make use of your results in parts (a) and (

Banasree · Accepted Answer

Solution  - 
1.a) Given Data - l = 300 mi, d = 20mi
CDF – 
Merged one
Separate one
PDF –
Merged one
Separate one
b) Plot the PDF and CDF of random variable R
1.c) Probability of earthquake R R>100

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...

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