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IAI Actuarial Core Principles · Actuarial Statistics · Bayesian inference: priors, posteriors, loss functions and credible intervals

The prior for a proportion p is Beta(a, b) with prior mean 0.25 and a + b = 12. After observing 6 successes in 18 trials, what is the posterior mean of p?

The prior has a = 3 and b = 9, so the posterior is Beta(9, 21) after adding 6 successes and 12 failures. Its mean is 9/30, or 0.3. This lies between the prior mean 0.25 and sample proportion 1/3.

  1. A9/30Correct
  2. B6/18
  3. C3/12
  4. D9/18
  5. 6/30

Explanation

a = 0.25 × 12 = 3, b = 9. Posterior is Beta(3+6, 9+12) = Beta(9, 21). Mean = 9/30 = 0.3. The option 6/18 is the data-only estimate.

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