Question
Could someone help me with this, thank you!! Exercise 6.19 (Sum of independent Poisson RV's is...
![Exercise 6.19 (Sum of independent Poisson RVs is Poisson). Let (Te)k1 be a Poisson process with (i) Use memoryless property to show that N(t) and N(t+s) - N(t) are independent Poisson RVs ) Note that the total number of arrivals during [0, t+s] can be divided into the number of arrivals rate λ and let (N(t)120 be the associated counting process. Fix t, s 0. of rates λ t and As. during [0, t] and [t, t + s]. Conclude that if X ~ Poisson(At) and Y ~ Poisson(As) and if they are independent, then X+Y e Poisson(X(t s](http://img.homeworklib.com/questions/ca4e5fb0-4ca4-11eb-b72c-4d5e61231c9a.png?x-oss-process=image/resize,w_560)
Could someone help me with this, thank you!!
Exercise 6.19 (Sum of independent Poisson RV's is Poisson). Let (Te)k1 be a Poisson process with (i) Use memoryless property to show that N(t) and N(t+s) - N(t) are independent Poisson RVs ) Note that the total number of arrivals during [0, t+s] can be divided into the number of arrivals rate λ and let (N(t)120 be the associated counting process. Fix t, s 0. of rates λ t and As. during [0, t] and [t, t + s]. Conclude that if X ~ Poisson(At) and Y ~ Poisson(As) and if they are independent, then X+Y e Poisson(X(t s
Answers
In the last line, I wrote "then", that should be "and". The point is that, the last statement in the question (ii) (which to be concluded) is true since N(t), N(t+s)-N(t) and N(t+s) follows poisson distribution.
In the last line, I wrote "then", that should be "and". The point is that, the last statement in the question (ii) (which to be concluded) is true since N(t), N(t+s)-N(t) and N(t+s) follows poisson distribution.Similar Solved Questions
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