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Q2)

Rewrite the following stochastic events in mathematical notation using a suitably defined random variable:

a. The probability that the deflection at the most critical element of a certain structure exceeds 1.80 inches is 0.85.

b. Of every 100 road construction projects, 28 experience two or more fatalities.

c. Twenty percent of the time, a certain aging engineering system component breaks down at least four times during operation every year.

d. Of all college students 75% read their campus newspaper at least once a week.

@3) and Q4) in pic 123123.jpeg

123123.jpeg

The following problems are from the course's textbook: Introduction to Civil Engineering
Systems, Samuel Labi, Wiley, 2014 (ISBN: 9780470530634)):
Question 1: Exercise 3, Textbook page 162.
Question 2: Exercise 6 on Text page 163.
Question 3.
The probability that Joe is late for work is 0.20. The probability that Joe drives fast to work is 0.40. The
probability that Joe performs well at work is 0.75. Choose 3 letters, say L, F, W, to denote each of these
events. If Joe is late, the probability that he drives fast to work is 0.9. Assume that his punctuality or
lateness to work does not influence whether he performs well at work that day. Furthermore, 30 out of
every 100 days, he drives fast to work and does a good job in the same day. (a) For all paired
combinations of these two events, comment on their mutual exclusivity, statistical dependence, or
statistical independence. Use the table below.
Pair
Property (circle one)
L and F
Mutually exclusive/Statistically dependent/Statistically independent
L and W
Mutually exclusive/Statistically dependent/Statistically independent
F and W
Mutually exclusive/Statistically dependent/Statistically independent
(b) Using the general probability equation and your prescriptions in (a) above, find the probability that on
any randomly selected day, ...
(i) either he is late for work or he drives fast to work or both happen.
(ii) either he is late for work or he performs well at work or both happen.
(iii) either he drives fast to work or he performs well at work or both happen
Question 4:
A. Indicate which of the following random variables are discrete and which are continuous:
i.
Whether or not users of a civil engineering system are satisfied with the system:
i.
The performance of a hydraulic system in terms of volume of water pumped per hour:
B. Rewrite the following stochastic events in mathematical notation using a suitably-defined
random variable
1.
Of every 100 road construction projects, 28 experience two or more fatalities.
ii.
20% of the time, a certain aging engineering system component breaks down at least 4 times
during operation every year.
C. Write in everyday English, the stochastic events that are represented by the
probabilities of the following random variables:
i.
a) p(Y >7) = 0.33
Y is a random variable representing the weekly number of hours worked
by a randomly selected Catholic University student.
ii.
b) p(F 2 2) = 0.85
F is a random variable representing the number of times a hydraulic
system gets overloaded

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Question 4 :"
A
i) Discrete variable
1 ) continous variable
B .
1 ) P ( F Z = 2 ) = 0 . 28
where I is fatality
1i ) P ( F > = 4 ) = 0. 2
( i) there is a 33%% Chance that a
catholic student...

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