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1714Optional Stopping as a p-Hacking MechanismA PM checks the p-value every hour and stops the experiment as soon as p < 0.05. Why does this inflate false positives?统计中等essay未尝试面试订阅1715The Prosecutor's Fallacy in a Trading ContextA rare anomaly occurs in only 1 out of 10,000 normal days. A model flags today's pattern as one that would happen with probability 1/10,000 under the null, and someone concludes the null must almost certainly be false. What key base-rate issue are they missing?统计中等essay未尝试面试订阅1716Replication Probability Is Not 1 - pA researcher says: ‘This alpha had p = 0.04, so replication next quarter is 96% likely.’ Why is that interpretation invalid?统计简单essay未尝试免费1717Significant but Commercially UncertainA venue-routing tweak delivers p = 0.01, but the 95% confidence interval for annual savings is [10k, 1.2m]. Why should the team still be cautious?统计简单essay未尝试免费1718Best-of-50 Reporting Without AdjustmentA researcher tests 50 candidate features and only reports the one with the smallest p-value, which happens to be 0.01. Why is it misleading to present 0.01 as if it came from a single pre-specified test?统计中等essay未尝试面试订阅17190.049 vs 0.051 Decision CliffTwo backtests differ only slightly: one reports p = 0.049 and the other p = 0.051. Why is it bad practice to call one ‘real’ and the other ‘not real’ purely because one is below 0.05?统计简单essay未尝试免费1720Low Prior Probability and Positive Predictive ValueSuppose only 1% of tested trading ideas are genuinely predictive. A testing pipeline has 80% power and a 5% false-positive rate. Conditional on obtaining a positive result, what fraction of positives are truly real?统计中等derivation未尝试面试订阅1721Switching to One-Sided After Seeing the SignA two-sided test is not significant, but the estimated coefficient has the expected sign. The analyst then reports the one-sided p-value instead. Why is that invalid if the direction was chosen after looking at the data?统计中等essay未尝试面试订阅1722Cherry-Picked EndpointA note tests 12 strategy diagnostics but highlights only the one with p = 0.02. What trap should the reviewer flag?统计简单essay未尝试免费1723Underpowered Winner’s CurseA sparse signal library was screened on short samples; the surviving signal is significant but came from a very low-power environment. Why should its in-sample effect size be viewed skeptically?统计中等essay未尝试面试订阅1724Conditioning Direction ErrorA reviewer writes: ‘p = 0.07 means the null hypothesis is true with probability 7%.’ What is wrong with the conditioning direction?统计简单essay未尝试免费1725Fail to Reject vs AcceptAn experiment does not reject the null at 5%. The team writes ‘the null is accepted.’ What is the correct correction?统计简单essay未尝试免费1756Backing Out Omitted Covariance From a Slope DropA desk regresses slippage Y on inventory pressure X. Without an urgency control, the OLS slope on X is 0.90. After adding a perfect measure of urgency U, the slope falls to 0.60. Suppose the structural model is Y = beta X + 0.5 U + noise and Var(X)=1. What is Cov(X,U)?统计简单derivation未尝试免费1757Recovering Signal-to-Noise From Two Attenuated SlopesA latent factor X* is measured twice: X1 = X* + e1 and X2 = X* + e2, where e1 and e2 are independent classical errors with the same variance and are independent of X*. Regressing Y on X1 alone gives slope 0.80. Regressing Y on the average (X1+X2)/2 gives slope 1.00. Under the same true structural slope beta, what is Var(X*)/Var(e)?统计简单derivation未尝试免费1758Selection-on-Survivors Bias in Strategy EvaluationA desk only records post-launch performance for strategies that first clear an internal backtest hurdle. Why does regressing realized performance on backtest score inside the launched set generally fail to recover the unconditional relationship?统计中等derivation未尝试面试订阅1759Averaging Two Noisy MeasurementsAgain the structural model is Y=2X+u with E[u\mid X]=0, but now you observe two noisy proxies: W 1=X+\eta 1, \qquad W 2=X+\eta 2, where \eta 1,\eta 2 are independent of each other and of X,u. Suppose Var (X)=4 and each noise term has variance 1. If you regress Y on the average proxy W=(W 1+W 2)/2, what is the probability limit of the slope?统计中等derivation未尝试面试订阅1760Wald Ratio With an Explicit Sign ConventionAn exchange latency shock Z in 0,1 moves the fraction of aggressive orders from 0.30 when Z=0 to 0.18 when Z=1, and average slippage from 4.2 bps when Z=0 to 5.4 bps when Z=1. Using the consistent orientation Delta Y / Delta X = (E[Y|Z=1]-E[Y|Z=0]) / (E[X|Z=1]-E[X|Z=0]), what Wald IV estimate do you get for slippage per one-unit increase in aggressive-order fraction?统计中等derivation未尝试面试订阅1761Direct and Total Effect After a Routing Channel SplitA routing signal X increases child-order fragmentation M by 2 units on average. The outcome obeys Y = 1.3 X + 0.4 M + noise, with X otherwise exogenous. What coefficient on X would you expect in a regression that controls for M, and what total effect of a one-unit increase in X would appear in a regression of Y on X alone?统计简单derivation未尝试免费1762A Tiny First Stage Is a Weak-Instrument WarningTwo candidate rollouts have the same reduced-form impact on PnL: E[Y\mid Z=1]-E[Y\mid Z=0]=0.02. For rollout A, the first stage is 0.20; for rollout B, the first stage is 0.01. Which rollout creates the weaker IV design, and why?统计中等multi part未尝试面试订阅1763Which Proposed Instrument Is More Plausible?You want to estimate the causal effect of quote-update intensity X on realized spread capture Y. Candidate instrument A is a randomized gateway assignment decided by the exchange. Candidate instrument B is same-day order-flow imbalance, which also directly moves spread capture. Which candidate is more plausible as an instrument, and what IV condition fails for the other one?统计中等multi part未尝试面试订阅