Anthony King M3.2 Collaborative Corner
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Embry-Riddle Aeronautical University *
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515
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English
Date
Dec 6, 2023
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docx
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Uploaded by kingalusmc
1
Module 3.2: Collaborative Corner
Anthony King (Team 3)
College of Aeronautics, Embry-Riddle Aeronautical University
SYSE 515: Math Applications in Systems Engineering
Federica Robinson-Bryant Instructor
October 29, 2023
2
Module 3.2: Collaborative Corner
Set 1, Exercise 11 -
The occurrences of strong motion earthquakes in an area are modeled using Poisson
distribution function. The historical data shows that in the past 40 years there were two
such earthquakes that occurred in the area.
Breakdown: r = 2, t = 40,
=
r/t
(2 / 40) =
0.05, (0.05)(10 years) =
0.50, (0.05)(1 year) =
0.05
a. Compute the probability that there will be no such earthquake in the area in the
next 10 years
.
Breakdown: r = 2, t = 40,
=
r/t, (2 / 40) = 0.05, 0.05(10) = 0.50
Solution: ((
t)
x
/ x!)(e
-
t
) = (((0.05)(10))
0
/ (0!))(e
-0.05(10)
) = (1)(0.60653066) =
60.7% probability
no such earthquake will occur within the next 10 years.
b. Compute the probability that such an earthquake may occur next year.
Solution: (((.05)(1))
1
/ (1!))(e
-0.05(1)
) = (0.05)(0.951229425) = 0.047561471 =
4.8% probability
that such an earthquake will occur next year.
c. If a strong motion earthquake occurs in the area, there is a .01 probability that a
dam located in the area will suffer damage. Compute the probability of damage
to the dam in the next 10 years due to earthquakes.
Note: Use formula: (e
-
)(
)
x
/ (x!) & know that
= (.01)(0.5) =
0.005
Solution: (e
-0.005
)(0.005)
0
/ (0!) = 0.995012479
1 - 0.995012479 = 0.004987521
There’s a 0.499 % probability that a dam located in the area will be damaged from possible
earthquakes within the next 10 years. Half of 1% probability.
3
References
Amekudzi, A., Khisty, C., Mohammadi, J. (2012).
Systems Engineering with Economics,
Probability, and Statistics
(2
nd
ed.). J. Ross Publishing.
Richardson, W. & Wortman, B. (2018).
Certified Reliability Engineer Primer
(5
th
ed.). Quality
Council of Indiana.
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