answer questions A-E

A. The two main purposes of "pooling" by insurance companies are to spread the losses incurred by the few over the entire group and to substitute actual losses by average losses . This mean losses can be more accurately predicted based on the law of large numbers which reduces the uncertainty or risk For all of the following questions, assume that a single homeowner has a home that is worth $50 (to keep the math simple) and the chances that the home will be totally lost to a peril in a given year is 10% meaning there is a 90% chance that the home will NOT have a catastrophic event and will still be worth $50 at the end of the year . What is the expected loss for the year (no dollar sign needed)?

B. What is the standard deviation of the expected loss (no dollar sign needed)?

C. If another homeowner with an identical home joins with the first homeowner to pool (combine) their loss exposures (with each home independent of the other) and each agrees to pay an equal share of any loss that might occur, what are the four possible outcomes with probabilities for each home owner? Probability that neither home is lost Probability that only the first home is lost : Probability that only the second home is lost: Probability that both homes are lost: Enter all answers as a decimal .

D. With the second home added to the "pool", what will be the probable (or expected) dollar loss for each of the two homeowners for the year? (no dollar sign needed)

E. With the two homes combined , what will be the standard deviation of the expected dollar loss for each of the homeowners ? (no dollar sign and rounded to two decimal points)