Revision as of 21:17, 8 May 2023 by Admin (Created page with "Individuals purchase both collision and liability insurance on their automobiles. The value of the insured’s automobile is ''V''. Assume the loss ''L'' on an automobile clai...")
May 08'23
Exercise
Individuals purchase both collision and liability insurance on their automobiles. The value of the insured’s automobile is V. Assume the loss L on an automobile claim is a random variable with cumulative distribution function
[[math]]
f(t) = \begin{cases}
\frac{3}{4}\left(\frac{l}{V}\right)^3, \, 0 ≤ l \lt V \\
1-\frac{1}{10}e^{\frac{-(l-V)}{V}}, \, \textrm{otherwise}
\end{cases}
[[/math]]
Calculate the probability that the loss on a randomly selected claim is greater than the value of the automobile.
- 0.00
- 0.10
- 0.25
- 0.75
- 0.90
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
May 08'23
Solution: B
[[math]]
\operatorname{P}(X \gt V) = 1-\operatorname{P}( X \leq V ) = 1-F(V) = 1- (1-\frac{1}{10}e^{-\frac{V-V}{V}}) = 0.10
[[/math]]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.