homework_04

Homework_04 - light normal heavy 0.25 0.40 0.15 1/30 1/35 1/55 bad bad bad light normal heavy 0.03 0.07 0.10 1/35 1/42 1/70 ∑ = 1.00 Find the

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MIT OpenCourseWare http://ocw.mit.edu 1.010 Uncertainty in Engineering Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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1.010 Fall 2008 Homework Set #4 Due October 9, 2008 (in class) 1. Calculate and plot the hazard function for the lifetime distribution shown below. 2. Read Application Example 7 and do the following: For a given suburb of Boston and a certain route, the commuting time D depends on traffic conditions T and weather W . Specifically, the random variable ( D | T , W ) has exponential distribution with parameter λ that depends on T and W . The probability of various combinations of T and W and the associated values of λ (in min -1 ) are: 0 2 t f T ( t ) 1 W T P [ T W ] λ (min -1 ) good good good
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Unformatted text preview: light normal heavy 0.25 0.40 0.15 1/30 1/35 1/55 bad bad bad light normal heavy 0.03 0.07 0.10 1/35 1/42 1/70 ∑ = 1.00 Find the probability density function of D , f D ( d ), using a relation analogous to Eq. 2 of Application Example 7. Plot this density function. Is it an exponential density? Calculate the unconditional probability that D >40 minutes? 3. The joint probability mass function of precipitation depth X (mm) at a raingauge station and flow Y (m 3 /s) of a nearby river is as follows: X =25 X =50 X =75 Y =2 0.05 0.12 0 Y =4 0.11 0.30 0.10 Y =6 0 0.12 0.20 a) Find the marginal PMFs of X and Y . b) If the raingauge indicates a precipitation of 50mm, what is the probability that the flow exceeds 4 m 3 /s?...
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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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Homework_04 - light normal heavy 0.25 0.40 0.15 1/30 1/35 1/55 bad bad bad light normal heavy 0.03 0.07 0.10 1/35 1/42 1/70 ∑ = 1.00 Find the

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