Actuarial Notes

SOA Exam P Sample Question 600

Study guide: Exam P-1

Hospitalization losses under a certain policy are mutually independent and each has cumulative distribution function

F(x) = \begin{cases}
0, & \text{for } x < 0 \\[4pt]
\dfrac{x + 15x^2}{16}, & \text{for } 0 \le x \le 1 \\[4pt]
1, & \text{for } x > 1
\end{cases}

For each hospitalization loss, the insurer reimburses up to a maximum of 0.80.

Calculate the probability that a policyholder's first partially unreimbursed hospitalization loss occurs on the third hospitalization.

  • A) 0.027
  • B) 0.080
  • C) 0.128
  • D) 0.148
  • E) 0.350

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