An insurance company designates 10% of its customers as high risk and 90% as low risk.
The number of claims made by a customer in a calendar year is Poisson distributed with
mean θ and is independent of the number of claims made by a customer in the previous
calendar year. For high risk customers, θ = 0.6, while for low risk customers θ = 0.1.
Calculate the expected number of claims made in calendar year 1998 by a customer who
made one claim in calendar year 1997.



My solution:

Given that claims made by a customer in a year are independent of those made in the previous year, I disregarded the 1997 claim filing.

For any year, the probability that a customer makes one claim would be -

f(k) = [0.1 * (e ^ -0.6) * (0.6 ^ k) / k! ] + [0.9 * (e ^ -0.1) * (0.1 ^ k) / k! ]

E(x) = ∑ xf(x)

works out to 0.1*0.6 + 0.9*0.1 = 0.15

doesnt match the key

I am way off here, i guess!