stat2303_assignment03_ans

07 b let and be the number of storms during the first

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a good year and a bad year, respectively. , 0.3 0.3 3 ! 0.3 , 0.7 3 ! , 3 ! 6 ! 0.7 6 ! 0.7 3 ! 0.3 6 ! 0.7 6 ! , , Hence, 0 does not have independent increments 0.7 0.3 0.3 , Hence, c) Since , 0.7 0 has stationery increments 0 does not have independent increment, it is not a Poisson process d) | , 1 1 1 3 3 0.3 0.3 0.5183 31 3! Page 5 of 7 3 31 3! 0.7 61 3! Semester 1, 2010­11 STAT2303/2803 Probability Modelling/Stochastic Models 6) a) Let and 2, respectively. , where and 0 are Poisson processes with rates 1 0 0 0 0 and , is also has independent increments Since is independent of is independent of 0 independent of 0 , i.e. Consider 2 ! ! ! ! ! 3 ! , 2 ! 0,1, … Hence the number of customers arrived follows a Poisson process rate 3 per minute. b) 30| 30, 30, 50 50 50 20 50 2 30! 20! 3 50! 2 50! 30! 20! 3 0.0705 Since | 50 50 , , 50 Page 6 of 7 50 , 0 with Semester 1, 2010­11 STAT2303/2803 Probability Modelling/Stochastic Models , 50 2 ! 50! ! 50 50 50 ! 3 50! 2 !3 1 3 Hence, | ~ Therefore, 50 100 3 2 3 | Page 7 of 7 50, 2 3 50...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online