# Practice - Dr Edwin Romeijn Practice Problem Set ESI 6321...

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Dr. Edwin Romeijn ESI 6321 Applied Probability Methods in Engineering Practice Problem Set Class of 2009 - 1 - ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OUTREACH ENGINEERING MANAGEMENT Class of 2009 PRACTICE PROBLEM SET Exercise 2.3 Suppose that there are 100 MBA students in the first-year class. Of these students, 20 of them have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience. Suppose that a first-year MBA student is selected at random. (a) What is the probability that this student has at least four years of work experience? (b) Suppose that you are told that this student has at least three years of work experience. What is the conditional probability that this student has at least four years of work experience? Exercise 2.9 There are 550,000 people in the US infected with HIV. Of these people, 275,000 are drug users, and the rest are not drug users. The total population of the US is 250 million. There are 10 million drug users in the US. The standard blood test for HIV infection is not always accurate. The probability that someone who is infected with HIV will test positive for HIV is 0.99. The probability that someone who is not infected with HIV will test negative for HIV is also 0.99. Answer the following questions, clearly stating any assumptions that you need to make. (a) Suppose that a randomly chosen person takes the standard blood test for HIV, and the outcome of the test is positive. What is the probability that this person is infected with HIV? Is your answer surprising? (b) Suppose that a randomly chosen drug user takes the standard blood test for HIV, and the outcome of the test is positive. What is the probability that this person is infected with HIV? Exercise 2.14 A construction job is comprised of two tasks, which we will call “task A” and “task B”. The two tasks are initiated simultaneously and their completion times are uncertain. The entire construction job is completed as soon as both tasks are completed. The possible outcomes for the completion times of task A and task B, and the associated probabilities, are given in the table below.

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Dr. Edwin Romeijn ESI 6321 Applied Probability Methods in Engineering Practice Problem Set Class of 2009 - 2 - Time to complete Task A (in weeks) Time to complete Task B (in weeks) Probability 1 1 0.07 1 2 0.27 1 3 0.06 2 1 0.13 2 2 0.31 2 3 0.16 Probabilities of time to completion of tasks A and B (a) What is the probability distribution of the duration of task A? of task B? of the job as a whole? (b) What is the mean and the standard deviation of the duration of task A? of task B? of the job as a whole?
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Practice - Dr Edwin Romeijn Practice Problem Set ESI 6321...

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