An Island is initially uninhabitated. Creatures arrive as a poisson process of rate a per month. Once there each creature produces offspring as a poisson process of rate b per month. Assume that the Poisson process for arrivals and births are all independent. Assume also that there are no deaths and no creatures leave the island. let X(t) be the number of creatures on the island at time t months and .
What is the probability that the island is inhabitated by time 3 months?
Do they mean there is at least one creature after 3 months? I have a formula for but I am not sure what is n=? when t=3.
thanks for any help.
In mathematical terms they want .
The previous post might be useful if you draw a Poisson process and see which each thing refers to.