exercise:Cb32047610: Difference between revisions
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F(l) = \begin{cases} | |||
\frac{3}{4}\left(\frac{l}{V}\right)^3, \, 0 ≤ l < V \\ | \frac{3}{4}\left(\frac{l}{V}\right)^3, \, 0 ≤ l < V \\ | ||
1-\frac{1}{10}e^{\frac{-(l-V)}{V}}, \, \textrm{otherwise} | 1-\frac{1}{10}e^{\frac{-(l-V)}{V}}, \, \textrm{otherwise} | ||
Latest revision as of 21:20, 8 May 2023
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(l) = \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.