The question asked is:
"Items coming off of an assembly line are inspected sequentially by two inspectors and declared to be defective (D) or non-defective (N). The two inspectors work in different rooms and cannot communicate with one another. State, with reasons, whether you think that the pairs of deci-sions made by the two inspectors on each item are dependent or independent"
I believe that it is independent since the workers are in different rooms and cannot communicate, therefore one cannot influence the other's decision.
However, the solution states that it is dependent since if one inspector declares the item defective then the other inspector has a higher probability of declaring that item defective because the quality of said item is poor. Think of a record kept of the pairs of decisions made by the inspectors as each item comes off the assembly line. You will see a higher proportion of (D1, D2) pairs than, say, (D1, N2) pairs.
Am I in the wrong or can both cases occur?
Best Answer
The pairs of decisions are dependent, exactly because when the first inspector flags an items as D, it will most likely actually be D, so that the second inspector will very likely flag it as D as well. So, knowing that the first inspector flagged it as D, the probability that the second inspector will flag it as D is different than without the knowledge that the first inspector flagged it as D. This is exactly what it means for two random variables to be dependent.
On the other hand you could say that the inspectors are independent, but this would not really be independent in a mathematical sense. It would reflect that the inspectors just judge the items by their own knowledge and do not have any (hidden) interest in aligning their decisions.