As well as following a Poisson process in time, we can also use a Poisson point process to model the location of volcanic eruptions in space. The Auckland volcanic field has a total area of 600 km2

. We know the next eruption will happen eventually, but we don’t know where. Assume it’s equally likely to be located at any point in the volcanic field.

a. What is the distribution of the location in space for the eruption that’s going to happen next?

b. My local board covers an area of 32 km2 within the volcanic field. What is the probability that the next eruption will take place in my local board area?