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

A loss X is lognormal with parameters μ = 5 and σ² = 0.64, meaning ln X is Normal(μ, σ²). What is E[X]?

E[X] equals e^5.32. For a lognormal, the mean is exp(μ + σ²/2), and with μ = 5 and σ² = 0.64 the exponent is 5 + 0.32. Using e^5 gives the median, and adding the full variance gives e^5.64, which is incorrect.

  1. Ae^5
  2. Be^5.64
  3. Ce^5.32Correct
  4. De^5.8
  5. e^5.4

Explanation

E[X] = exp(μ + σ²/2) = exp(5 + 0.32) = e^5.32. The option e^5.64 adds σ² instead of σ²/2, and e^5 is the median.

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