The random variable for a loss, X, has the following characteristics:

[math]x[/math]	[math]F(x)[/math]	[math]\operatorname{E}( X \wedge x ) [/math]
0	0.0	0
100	0.2	91
200	0.6	153
1000	1.0	331

Calculate the mean excess loss for a deductible of 100.

• 250
• 300
• 350
• 400
• 450

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: B

Mean excess loss =

[[math]] \frac{\operatorname{E}(X) - \operatorname{E}(X \wedge 100)}{1-F(100)} = \frac{331-91}{0.8} = 300 [[/math]]

Note that [math]\operatorname{E}( X ) = \operatorname{E}( X \wedge 1000)[/math] because [math]F(1000) = 1.[/math]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.