**8.1** For the excess loss variable,

For the left censored and shifted variable,

and it is interesting to note that the excess loss variable has an exponential distribution.

**8.2** For the per-payment variable,

For the per-loss variable,

**8.3** From Example 3.1 *E*(*X*) = 30,000 and from Exercise 3.9,

Also *F*(5,000) = 1 − 0.3*е*^{−0.00001(5,000)} = 0.71463, and so for an ordinary deductible the expected cost per loss is 28,536.88 and per payment is 100,000. For the franchise deductible, the expected costs are 28,536.88 + 5,000(0.28537) = 29,963.73 per loss and 100,000 + 5,000 = 105,000 per payment.

**8.4** For risk 1,

The ratio is then

As *k* goes to infinity, the limit is infinity.

**8.5** The expected cost per payment with the 10,000 deductible is

At the old ...

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