stat2303_assignment03_ans

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

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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...
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