IND ENG 161 Study Guide - Midterm Guide: Bayes Estimator, Fair Coin, Random Variable

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

Document Summary

Solutions for midterm 1: let xi be the indicator random variable taking value 1 if the ith contestant pulls out one or two red tickets, 0 otherwise. Also, let x denote the number of prizes given out. P {xi = 1} = 30p {x1 = 1} where the last equation comes from the fact that each contestant has the same probability of getting at least one red ticket. P {x1 = 1} = 1 p {x1 = 0} = 1 p {contestant 1 pulls out 2 black tickets} = 1 . 100 99 since there is no replacement. E[x] = e[x|f ]p {f } + e[x|b]p {b} P {x = 4|f }p {f } + p {x = 4|b}p {b} 1: let x denote the number of ips jack makes, y the number of ips jill makes. We have x and y are geometric random variables with parameters 0. 5 and p respectively.