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

Claim sizes X follow a Gamma distribution with shape α = 4 and rate λ = 0.02 per rupee thousand. Claims are scaled to Y = 3X (a change of units). What are the mean and variance of Y?

Mean 600 and variance 90,000. For X, the mean is 4/0.02 = 200 and the variance is 4/0.0004 = 10,000. Multiplying by 3 multiplies the mean by 3 and the variance by 9. Forgetting to square the factor gives 30,000, which is wrong.

  1. AMean 600, variance 90,000Correct
  2. BMean 200, variance 10,000
  3. CMean 600, variance 30,000
  4. DMean 600, variance 270,000
  5. Mean 66.67, variance 1,111

Explanation

For X: mean = α/λ = 200, variance = α/λ² = 4/0.0004 = 10,000. For Y = 3X: mean = 600, variance = 9 × 10,000 = 90,000. The option with 30,000 forgets to square the factor 3, and 270,000 wrongly multiplies by 27.

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