13. Consider an initial insurance portfolio of 20,000 independent automobile policies, each with a standard deviation of $300 and an expected loss of $400. Now suppose that this insurer also writes 1,000 independent fire insurance policies in order to diversify its line base. Each fire policy covers fairly large industrial risks, with an expected loss of $12,000 and a standard deviation of $15,000.

1. a) Calculate the expected value and standard deviation of average loss per policy for the entire insurance portfolio.

2. b) Calculate the ruin probability, assuming the firm estimates that its reserves and surplus permit it to meet claims up to $21 million in total (i.e., $1,000 per policy).

3. c) Now assume that these policies are not independent; the correlation coefficient between

   any two auto policies is 0.05, and the correlation coefficient between any two fire policies is also 0.05; there is no correlation between auto and fire policies. Calculate a) and b) again.