A health insurance company classifies individuals as "healthy" or "unhealthy". 58% of individuals are healthy. Annual aggregate claims for healthy individuals follow a Pareto distribution with parameters = 2.5 and = 1,800 (mean 1200, variance 7,200,000). Annual aggregate claims for unhealthy individuals follow a Pareto distribution with parameters = 7 and = 12, 000 (mean 2,000, variance 7,000,000).

a) A particular individual claimed a total of $1,020 last year. Calculate the expectation and variance for this year's aggregate annual claims for this individual.

b) What aggregate claims for last year would make the variance of this year's claims largest?