How many orders are resting at the level

Limit orders arrive at one price level as a Poisson process at rate 5 per minute. Each order rests until it is cancelled, and the resting times are independent $\text{Exponential}$ with mean 2 minutes, independent of the arrivals. Ignore fills. The level is empty at time 0.

(a) What is the distribution of the number of orders resting at time $t$?

(b) At $t = 2$ minutes, what are the mean number of resting orders and the probability that the level is empty?

(c) What is the long-run distribution?

(d) Suppose instead every order rests for exactly 2 minutes. How do the answers to (b) and (c) change?