In a certain region, there is an average of 0.6 ant nests per square kilometre and an average of 0.3 beehives per square kilometre. Suppose that the locations of ant nests are independent of other ant nests, the locations of beehives are independent of other beehives, and the locations of ant nests and beehives are independent of each other.

D) N follows an exponential distribution with = 0.6 and H follows an exponential distribution with = 0.3.

e) Derive the expressions for probability distribution functions of and from the probabilities of observing certain counts of ant nests and beehives.

Hint: Counts of nests/beehives and the area covered to find nests/beehives are different variables. Note: you may not use the answer from (d) to simply state what the distribution is.

You must derive the same answer independently from (d)