 Solution

Keep the true parameter fixed and imagine repeatedly collecting four independent and identically distributed observations under the same model. Compute the maximum-likelihood estimate, its estimated standard error, and the Wald confidence interval afresh each time. The intended coverage statement is that approximately 95% of those random confidence intervals contain the fixed true parameter, provided the normal approximation is adequate.

After these particular observations have been collected, both endpoints are fixed. The frequentist statement does not assign 95% probability to the fixed parameter lying between these particular endpoints. Nor does the confidence interval describe the range containing 95% of future observations. The small sample makes the nominal 95% coverage an approximation whose accuracy is not guaranteed.