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