IND ENG 161 Study Guide - Midterm Guide: Random Variable

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

Document Summary

1. (a) poisson arrivals take exponential amount of time. Thus, arrival of the rst man is an exponential with rate = 2 and the arrival of the rst woman is exponential with. Therefore, the probability the rst arrival is a man is. + = 2 (b) exponential random variables are memoryless, so the probability of a male arriving. Therefore, the probability before a female at any point in the process will be 2. E[x] = e[x|y = 0]p (y = 0) + e[x|y = 1]p (y = 0) 2. (a) a mean time of 0. 75 means the rate of the exponential is pletion time of student i be denoted by ti where ti exp( 4 probability the ith student nishes early is. P (ti < 1) = 1 e . Let xi = 1 if the ith student leaves early and xi = 0 otherwise. P (xi = 1) = 1 e .