Assignment 4 - CE 93 – Engineering Data Analysis Prof....

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Unformatted text preview: CE 93 – Engineering Data Analysis Prof. Joan Walker, Spring 2011 Assignment 4 Due on 2/23/2011 at the beginning of class 1. Problem 3.38 in Ross. Note: There is a typo—the questions (a) and (b) appear above the problem number and definition. 2. Problem 3.41 in Ross. 3. Problem 3.47 in Ross. 4. Bill and George go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with probability 0.7, whereas George, independently, hits the target with probability 0.4. a. Given that exactly one shot hit the target, what is the probability that it was George’s shot? b. Given that the target is hit, what is the probability that George hit it? 5. A gross polluter detection system consists of two sensors, A and B, and is used to identify motor vehicles that are gross polluters. Sensor A detects such vehicles with 70% probability, while sensor B does so with 90% probability. Sensor A never incorrectly detects a non‐gross‐polluting vehicle. Sensor B has a false alarm rate of 1%, i.e., 1% of vehicles that are not gross polluters are registered as gross polluters by Sensor B. 5% of the vehicles passing through the detection system are gross polluters. a. Suppose only sensor A is installed, and does not detect that a particular vehicle is a gross polluter. What is the probability that this vehicle actually is a gross polluter? b. Suppose only sensor B is installed and it does detect that a particular vehicle is a gross polluter. What is the probability that this vehicle actually is a gross polluter? c. Now suppose both sensors are installed, and that the events of A and B correctly detecting a gross polluting vehicle are statistically independent. i. What is the probability that a gross polluter vehicle will be detected by both sensors? ii. What is the probability that a gross polluter vehicle will be detected by at least one of the two sensors? d. Suppose the system is configured so that it registers a vehicle as grossly polluting if either sensor detects it to be so, but does not indicate which of the individual sensors has detected it. i. If the system detects a vehicle as a gross polluter what is the probability that 1. Only Sensor A detected it? 2. Only Sensor B detected it? 3. Both sensors detected it? ii. What is the false alarm rate for this system—i.e. the probability that a non‐ gross‐polluter vehicle will be registered as a gross‐polluter? CE 93 – Engineering Data Analysis Prof. Joan Walker, Spring 2011 6. The duration (in hours) of two repair activities A and B on the Bay Bridge are denoted as TA and TB. TA and TB are statistically independent. Their probability mass functions (PMFs) are given in the table. Activity B begins as soon as Activity A has been completed. Plot the PMF of the total duration T, which is required to complete both activities. Note: You can plot the PMF either by hand or by computer, but for full credit on this problem, you should calculate the probabilities by hand. Activity A Hours (t) p(TA=t) 6 0.2 7 0.5 8 0.3 Activity B Hours (t) p(TA=t) 7 0.3 8 0.3 9 0.4 ...
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This note was uploaded on 06/02/2011 for the course CIV ENG 93 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.

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