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University of the Philippines – Diliman
Department of Industrial Engineering and Operations Research
IE 143 Long Quiz 1
Long Quiz 1 Review Problems
1.
Your driving time to work is between 30 and 45 minutes if the day is sunny and between 40 and 60 minutes
if the day is rainy, with all times being equally likely in each case. Assume that a day is sunny with
probability 2/3 and rainy with probability 1/3.
(a)
Find the PDF, the mean, and the variance of your driving time.
(b)
On a given day your driving time was 45 minutes. What is the probability that this particular day was
rainy?
(c)
Your distance to work is 20 miles. What is the PDF, the mean, and the variance of your average speed
(driving distance over driving time)?
2.
The random variables X and Y have the joint PDF
g
G,±
²³, ´µ = ¶
2,
·g ³ > 0 ¸¹º ´ > 0 ¸¹º ³ + ´ ≤ 1,
0,
»¼ℎ½¾¿·À½.
Let A be the event {Y
≤
0.5} and let B be the event {Y > X}. Calculate P(BA).
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 Spring '11
 a
 Operations Research

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