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4123Spread-Impact Decomposition 3A buy slice arrives when the mid is 80.2. Crossing the spread costs 0.03 dollars per share, temporary impact is 0.04, and permanent impact is estimated at 0.015. What are the expected average fill price and the post-trade mid immediately after the market digests the permanent impact?金融与交易中等数值题未尝试面试订阅4126Square-Root Impact Scaling 1A desk uses a square-root impact rule: cost in bps scales with sqrt(Q/ADV). A trade of 1.00\% of ADV costs 8 bps. What impact cost would the same model predict for a trade of 4.00\% of ADV?金融与交易简单数值题未尝试面试订阅4131VWAP Schedule in a Liquidity-U-Shaped DayYou need to buy 6% of daily volume in a liquid index future by the close, and the PM is benchmarked strictly to day-long VWAP rather than arrival. Which schedule is the most natural starting point?金融与交易中等derivation未尝试面试订阅4132Alpha Decay and Front-LoadingA signal is expected to decay within the next 20 minutes, and waiting is more expensive than crossing a bit more spread now. Should the schedule become more or less front-loaded?金融与交易中等derivation未尝试面试订阅4133Low-Signal Passive LiquidationYou need to liquidate a medium-size position over several days with no urgent alpha and strong concern about footprint. Which scheduling style is the better default: high-POV aggression or a lower-participation passive schedule?金融与交易中等derivation未尝试面试订阅4134Closing Auction Use CaseA benchmarked portfolio must minimize tracking error to the official close, and the stock has deep closing-auction liquidity. Which venue or schedule component becomes especially attractive?金融与交易中等derivation未尝试面试订阅4135Participation Cap in Thin NamesIn a thin name, why might a trader impose a strict maximum participation rate even when the order is behind schedule?金融与交易中等derivation未尝试面试订阅4136Why Quoted Spread Understates True CostWhy can quoted spread be a poor summary of true execution cost for a real institutional order?金融与交易中等essay未尝试面试订阅4137Why Passive Orders Can Still Lose MoneyWhy is it wrong to think that passive orders are always cheap just because they do not cross the spread?金融与交易中等essay未尝试面试订阅4138Why Impact Models Need a Urgency TermWhy is an execution problem incomplete if it models market impact but ignores alpha decay or urgency?金融与交易中等essay未尝试面试订阅4139Why Dark Liquidity Is Not Free LiquidityWhy can dark-pool access reduce displayed footprint and still fail to lower true cost much?金融与交易中等essay未尝试面试订阅4141Generative Threshold from Equal-Variance Gaussians 1A discriminative model was trained at class prior P(Y=1)=0.5 and outputs posterior probability 0.7 for a case x. Overnight the base rate shifts to P(Y=1)=0.2, while the class-conditional evidence for x is assumed unchanged. What posterior probability should you use after this pure prior shift?机器学习中等数值题未尝试面试订阅4146Naive Bayes Posterior 1A generative regime model assigns posterior probability P(trend|x)=0.7 to the trend regime. If the next-day expected payoff is 12 bps in trend and -4 bps in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4148Naive Bayes Posterior 3A generative regime model assigns posterior probability P(trend|x)=0.6 to the trend regime. If the next-day expected payoff is 0.015 return units in trend and -0.01 return units in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4149Naive Bayes Posterior 4A generative regime model assigns posterior probability P(trend|x)=0.4 to the trend regime. If the next-day expected payoff is 3 return units in trend and 1 return units in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4150Naive Bayes Posterior 5A generative regime model assigns posterior probability P(trend|x)=0.8 to the trend regime. If the next-day expected payoff is -2 bps in trend and 5 bps in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4151Generative Classification with a Missing Feature 1A two-feature naive Bayes model was trained generatively, but at prediction time X2 is missing. Prior P(Y=1)=0.5, P(X1=1|Y=1)=0.8, P(X1=1|Y=0)=0.3, P(X2=1|Y=1)=0.75, P(X2=1|Y=0)=0.4. You only observe X1=1. What posterior P(Y=1|X1) should the generative model use?机器学习中等数值题未尝试面试订阅4156Small Labeled Sample with Plausible StructureFor an observation x, a generative model summarizes the evidence as likelihood ratio p(x|Y=1)/p(x|Y=0) = 5. If the prior probability of class 1 is 0.2, what posterior probability P(Y=1|x) follows, and what 0.5-threshold decision does that imply?机器学习中等derivation未尝试面试订阅4157Lots of Labels but Misspecified Density StoryFor an observation x, a generative model summarizes the evidence as likelihood ratio p(x|Y=1)/p(x|Y=0) = 0.5. If the prior probability of class 1 is 0.4, what posterior probability P(Y=1|x) follows, and what 0.5-threshold decision does that imply?机器学习中等derivation未尝试面试订阅4161Why Naive Bayes Can Work Despite Wrong IndependenceYou have only a few hundred labeled observations, but domain knowledge gives a plausible class-conditional structure and you also have many unlabeled feature vectors. Would you start with a generative or a discriminative model first?机器学习中等essay未尝试面试订阅