Hello guys

I consider a linear growth birth and death process for a population with immigration, this leads me to define the growth parameter as $\displaystyle g = i + k_1\cdot n$ and death parameter as $\displaystyle d = k_2\cdot n$ for $\displaystyle i>0, \: k_1 < k_2$ and $\displaystyle n$ is the current population.

I then have no problem doing the first couple of questions regarding the mean, variance and long run distributions. But, I then need to find an expression for the long run time that the the size of the population is less than some number $\displaystyle N$, which stumbles me as it does not regard probabilities directly.

Kind regards