Compute posterior and event counts in fraud screen
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This question evaluates a candidate's competence in probability and statistical inference, covering binomial probability calculations, Bayes' theorem for posterior probability, rare-event base-rate reasoning, and modeling of correlated binary signals in a fraud-screening context.
Fake-account screening uses five independent signals per account. For fake accounts, each signal fires with probability 0.8; for authentic accounts, 0.05. An account is flagged if at least k signals fire. (a) For k=2, compute P(flagged | fake) and P(flagged | authentic) using the binomial distribution. (b) Assume base rate P(fake)=1.5%. Compute P(fake | flagged) via Bayes theorem and the expected number of flagged accounts in a day with 5,000,000 accounts scanned. Is a manual review queue of 80,000 per day sufficient? (c) Find the smallest k such that expected flagged volume fits within 80,000 ±5% while maximizing P(fake | flagged). Show work and justify the trade-off between precision and recall. (d) If signals are not independent and have pairwise correlation 0.2 within class, how would your answers and assumptions change?
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