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

Claim size X is lognormal with parameters mu = 8 and sigma^2 = 0.5 (so ln X ~ N(8, 0.5)). What is E[X]?

E[X] equals exp(8.25). For a lognormal variable the mean is exp(mu + sigma squared over two), so with mu 8 and variance 0.5 the exponent is 8 plus 0.25. The value exp(8) is the median, not the mean.

  1. Aexp(8.25)Correct
  2. Bexp(8.5)
  3. Cexp(8)
  4. Dexp(8.5) − exp(8)
  5. exp(9)

Explanation

E[X] = exp(mu + sigma^2/2) = exp(8 + 0.25) = exp(8.25). exp(8.5) wrongly adds sigma^2 rather than half of it. exp(8) is the median.

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