mini_quiz_2

mini_quiz_2 - individuals after 3 time periods. Problem 2...

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MIT OpenCourseWare http://ocw.mit.edu 1.010 Uncertainty in Engineering For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Fall 2008
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1.010 – Mini-Quiz #2 (45 min – open books and notes) Problem 1 (40 Points) A community of bacteria initially includes 1000 individuals. Given favorable conditions (light, temperature, nutrients), the community doubles in size during a unit time period, for example one day. If conditions are unfavorable, the community downsizes by a factor of 2. Suppose that favorable conditions occur with probability 0.6, and unfavorable conditions with probability 0.4, and that favorable/unfavorable conditions are independent in different time periods (days). Find the probability mass function of the number of
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Unformatted text preview: individuals after 3 time periods. Problem 2 (20 Points) At a given site, flood-producing storms occur infrequently. Considering the three conditions under which a point process is Poisson, state reasons for or against modeling the storm arrival times as a Poisson point process. Problem 3 (40 Points) The lifetime T of electric bulbs (e.g. the number of hours in operation before they fail) has an exponential distribution with cumulative distribution function: t 1000 1 T e 1 ) t ( F = for , with t in hours. t Suppose you have used a bulb for 500 hours without failure. Find the probability that the bulb will last at least 500 more hours. Hint: Use P[A|B] = P[A B]/P[B], with appropriately defined events A and B....
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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mini_quiz_2 - individuals after 3 time periods. Problem 2...

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