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2 Page 3 of 5 1 Semester 1, 201011 STAT2303/2803 Probability Modelling/Stochastic Models 4) Let , 0 be a Poisson process with rate . Calculate independent increments stationary increments
1 Page 4 of 5 Semester 1, 201011 STAT2303/2803 Probability Modelling/Stochastic Models , 5) Suppose that
a) Show that 0 and , , Let 0 are independent Poisson processes with 0 is also a Poisson process with rate
0 0 0 0 0
has independent increments Since is independent of
is independent of
Consider ! !
, 0,1, … Hence
0 is a Poisson process with rate
conditions for Poisson process. as it satisfies the three b) Show that the probability that the first event of the combine process comes from
, which does not depend on the time of the event
Let | Page 5 of 5 ~ exp occurs, i.e. be the waiting time until the first event of...
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