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(CIVL181)[2010](s)midterm~wmma^mock_10060.pdf
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CIVL181 C Spring 2010 - HKUST Mock Midterm Lecturer: JP Wang
1) (20%)
X and Y are independent random variables, their PDFs are:

0
...
10





1

x
fX (x)
=

otherwise
10





1

0
Let Z = X + Y, find a) FZ(z) when z < 0 b) FZ(z) when 0 z 1
...
y
fY ( y)
=

otherwise
2) (10%)
Using a Vann diagram to show the expression

AB

=

1

.

(

A

UB

)

3) (20%)
The return period of tornados with extreme wind load is 18 months following the Poisson distribution. A structure will be damaged if it is subjected to such tornados more than 2-time a year. Find
a) what is the probability of the structure that is damaged every year b) if the structure has a design life of 30 years, what is the probability that the structure remains intact during its structural life?
4) (30%)
In the CIVL181 class, there are 10 female students out of 110 students. Assume the probability for male and female students wearing earrings is 5% and 50%. Find
a) The probability that a random selected student who is not wearing earrings? b) The probability that a random selected students is male and wearing earrings? c) Among the students who wear earrings, the probability that a male student is
selected?
5) (20%) Let X and Y be discrete R.V. with joint PMF as: .1/4 (x, y) = (.4,1),(4,.1),(2,2),(.2,.2)
p(x, y) =.
0 otherwise
. Find the correlation coefficient, xy