An insurance company charges a customer an annual premium of $100, and there is a probability of 0.9 that the customer will not need to make a claim. If the customer does make a claim, the amount of the claim $X has a probability density function

for 0 ‰¤ x ‰¤ 1800. Each customer also incurs administrative costs to the insurance company of $5. If the insurance company has 10,000 customers, what is its expected annual profit? Would you expect the customers' claims to be independent of each other?