Chapter 18.2, Problem 27E

Losses After Deductible A manufacturer’s annual losses follow a distribution with density function

$f\left(x\right)=\{\begin{array}{l}\frac{2.5{\left(0.6\right)}^{2.5}}{x^{3.5}}\text{for }x>0.6\\ 0\text{otherwise}\text{.}\end{array}$

To cover its losses, the manufacturer purchases an insurance policy with an annual deductible of 2. What is the mean of the manufacturer’s annual losses not paid by the insurance policy? Choose one of the following. (Hint: The loss not paid by the insurance policy will equal the actual loss if the actual loss is less than the deductible. Otherwise it will equal the deductible.) Source: Society of Actuaries.

  (a) 0.84    (b) 0.88    (c) 0.93    (d) 0.95    (e) 1.00