 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-2/6h/d/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 6H / d / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

n \to \infty

m_{n} - \overline{X} = \frac{σ ^{2} ( μ - X )}{n ν ^{2} + σ ^{2}} = O_{p} (n^{- 1}),

(1)

while

v_{n} = \frac{σ}{n} (1 + \frac{σ ^{2}}{n ν ^{2}})^{- 1/2} \sim \frac{σ}{n} .

(2)

Thus the credible interval and confidence interval have asymptotically equal centres and half-widths, and both contract around the true parameter. Their interpretations remain different: the confidence statement concerns repeated samples, whereas the credible statement concerns posterior probability. This is normal-normal conjugacy with known observation variance.

 Read the full article

 New to topics? Read the docs here!