Expected co-occurrences for events A and B (computed under the assumption that the two events are independent) are largely different from observed co-occurrences for these two events. What conclusion can you make? Choose one best answer:

Question

BlackTom AI · Accepted Answer

Consider the scenario: we compute the expected co-occurrences of events A and B under the assumption that they are independent, and we find that these expected values are far from what is actually observed. 
Option 1: 'Events A and B are associated' — This aligns with the idea that independence implies that the occurrence of A provides no information about B. If the observed co-occurrences deviate from the independence-based expectation, it suggests a relationship between the events, i.e., they are associated or correlated in some way. 
Option 2: 'Events A and B are not associated' — This would be true if the observed co-occurrences matched the expected co-occurrences under independence. Since the problem states they are largely different, this option contradicts the observed discrepancy and is thus incorrect. 
Option 3: 'You can’t make any conclusions from this piece of information' — The mismatch between observed and expected under independence provides evidence about association; dismissing this would ignore the information provided by the comparison, so this is not a valid conclusion. 
In summary, the key takeaway is that a substantial difference between observed co-occurrence and the independence-based expectation indicates a relationship between A and B, pointing toward association rather than independence.

Expected co-occurrences for events A and B (computed under the assumption that the two events are independent) are largely different from observed co-occurrences for these two events. What conclusion can you make? Choose one best answer:单项选择题

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