Volcanic eruptions in the Auckland region are modelled using a Poisson distribution with rate = 1

Volcanic eruptions in the Auckland region are modelled using a Poisson distribution with rate λ = 1 eruption every 1000 years. Let Y ∼ Poisson(1). Which of the following statements gives the correct interpretation of Y?

a. Y is the number of eruptions that occur in a 1000-year period.

b. Y is the number of years we have to wait before an eruption occurs.

c. Y is the number of 1000-year intervals before an eruption occurs.

d. Y is the average number of eruptions per 1000-year period.