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IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples

The time to settlement of a claim (in days) is exponential with mean 20 days. Given that a claim has already remained unsettled for 30 days, what is the probability that it remains unsettled for more than 50 days in total?

The probability is e^(-1). The exponential distribution is memoryless, so the extra 20 days beyond day 30 has the same probability as a fresh claim lasting over 20 days, which is e^(-20/20). Using e^(-2.5) ignores the conditioning.

  1. Ae^(-2.5)
  2. Be^(-1.5)
  3. Ce^(-1)Correct
  4. D1 − e^(-1)
  5. e^(-0.6)

Explanation

By the memoryless property, P(T > 50 | T > 30) = P(T > 20) = e^(-20/20) = e^(-1). The option e^(-2.5) ignores the conditioning and uses P(T > 50), while e^(-1.5) is P(T > 30).

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