An insurer offers a travelers insurance policy. Losses under the policy are uniformly distributed on the interval [0, 5].
The insurer reimburses a policyholder for a loss up to a maximum of 4.
Determine the cumulative distribution function, [math]F[/math], of the benefit that the insurer pays a policyholder who experiences exactly one loss under the policy.
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[[math]]F(x) = \begin{cases}
0, \, x \lt 0 \\
0.20x, \, 0 \leq x \lt 4 \\
1, \, x \geq 4
\end{cases}[[/math]]
[[math]]F(x) = \begin{cases}
0, \, x \lt 0 \\
0.20x, \, 0 \leq x \lt 5 \\
1, \, x \geq 5
\end{cases}[[/math]]
[[math]]F(x) = \begin{cases}
0, \, x \lt 0 \\
0.25x, \, 0 \leq x \lt 4 \\
1, \, x \geq 4
\end{cases}[[/math]]
[[math]]F(x) = \begin{cases}
0, \, x \lt 0 \\
0.25x, \, 0 \leq x \lt 5 \\
1, \, x \geq 5
\end{cases}[[/math]]
[[math]]
F(x) = \begin{cases}
0, \, x \lt 0 \\
0.25x, \, 1 \leq x \lt 5 \\
1, \, x \geq 5
\end{cases}
[[/math]]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
