Question

Events related to the Poisson process can be often described in two equivalent ways: in terms of numbers of arrivals during certain intervals or in terms of arrival times. The first description involves discrete random variables, the second continuous random variables.

Let N(t) be the number of arrivals during the time interval [0,t] in a Poisson process. Let Yk be the time of the k th arrival.

a) The event {N(5)>1} is equivalent to the event {Yk≤b} , for suitable b and k . Find b and k .

b=
unanswered
 
k=
unanswered
b) The event {2<Y3≤Y4≤5} is equivalent to the event {N(2)≤a and N(5)≥b} . Find a and b .

a=
unanswered
 
b=
unanswered

Answer 1

k=2
b) a=2

Answer 2

b = 5
k = 2
a = 2
b = 4