Actuarial Notes

SOA Exam P Sample Question 381

Study guide: Exam P-1

The lifetime (in years) of a car is a random variable with probability density function

f(x) = \begin{cases}
0.0625e^{-0.0625x}, & \text{for } x > 0 \\
0, & \text{otherwise.}
\end{cases}

Calculate the probability that the car's lifetime is less than 20 years, given that the car's lifetime is at least five years.

  • A) 0.445
  • B) 0.522
  • C) 0.608
  • D) 0.832
  • E) 0.975

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