An insurance company will sell a fire insurance policy for a house similar to mine for $1000 (for one year of protection). If there is not a fire at my house this year, the insurance company has made a $1000 profit. Their experience indicates that there is a .001 probability that I will have a 'total' loss fire costing them $301,000 (meaning that they collected $1000 from me at the beginning of the year, and paid $301,000 to rebuild my home and replace loss contents during the year- a huge loss for them). There is a 1% chance that I'll have a 'small' fire which will cause $41,000 in damages. Suppose that these are the only three possible outcomes in this simplified example.
a) Find the probability that the insurance company make a $1000 profit from the fire insurance policy that I buy for a given year.
b) Find the expected profit for the insurance company from the policy that I buy for a given year (the mean profit for mine and similar policies sold in a given year)
c) Find the standard deviation for your variable