Tropical cyclones are quite common in northern Australia during the summer months. Suppose the number of cyclones is Poisson distributed with a mean of 4.5 cyclones per season.

(a) What is the probability of having no cyclones over a season?

(b) What is the probability of having between 3 and 4 cyclones in a given season?

(c) What is the probability of having over 6 cyclones in a given season? If this actually occurred, could you make any conclusions to support the arguments for climate change? What might you conclude about lambda?