Suppose New Belgium Brewing Companys property losses have the following distribution.

Loss	Probability
$6,500,000	0.01
$4,000,000	0.01
$2,000,000	0.04
$700,000	0.08
0	0.86

a. What is the expected value of New Belgiums property losses (aka, the actuarially fair value of insurance)?

b. What is the standard deviation of New Belgiums expected property losses?

c. Suppose PC Inc, New Belgiums insurance carrier, charges a 40% load when determining its property and casualty insurance premiums. What would they charge New Belgium for property insurance, i.e., what will the premium be?

d. Assume that New Belgiums property losses are normally distributed (they arent, of course) with mean and standard deviation equal to the expected value and standard deviation you calculated in a. and b. What is New Belgiums probable maximum loss (PML) at the 95% level?[1] (critical value = 1.645)

e. Suppose New Belgium's CRO makes this assumption. Would the estimated PML underestimate or overestimate New Belgian's true PML? Why?