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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MIT OpenCourseWare 1.010 Uncertainty in Engineering For information about citing these materials or our Terms of Use, visit: Fall 2008
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online