IND ENG 161 Midterm: ieor161-sp2010-mt1-Lim-soln

• School: Berkeley
• Department: Industrial Engineering And Operations Research
• Course: IND ENG 161
• Professor: All

Document Summary

Midterm exam i, 2010: [10+10+10] there are 3 people on a sinking ship and they can jump one at a time onto a life-raft1. The ship will sink at a time determined by an exponential random variable with mean 1/ (i. e. rate ). The time taken for the 1st person to escape is an exponential r. v. with rate 1, while the 2nd person takes an exponential r. v. with rate. T : time taken for the ship to sink exp( ) Ti: time taken for the ith person to escape exp( i) N : number of people that escapes a) b) P (t > t1 + t2 + t3) = p (t > t1)p (t > t1 + t2|t > t1)p (t > t1 + t2 + t3|t > t1 + t2) = p (t > t1)p (t > t2)p (t > t3) by memoryless of exponential distribution.