IE143-LQ1revprob

# IE143-LQ1revprob - University of the Philippines Diliman...

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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(B|A).

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## This note was uploaded on 05/19/2011 for the course IE 2 taught by Professor A during the Spring '11 term at University of the Philippines Diliman.

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IE143-LQ1revprob - University of the Philippines Diliman...

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