Because the measurement can cross the threshold in both directions while the model declares dementia irreversible, one needs the diagnostic rule's sensitivity
$$
\mathbb P(X<10\mid\text{true dementia})
$$
and specificity
$$
\mathbb P(X\geq10\mid\text{no true dementia}).
$$
These quantify false negative and false positive state classifications and permit a hidden-state or misclassification model instead of treating every threshold crossing as the true irreversible onset.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 207 / 1 / b / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-207/1/b/i/solution