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1632Estimating Activity and Size in a Zero-Inflated Fill ModelConsider a toy fill-size model for a child order. With probability 1-p, no fill occurs and the observed size is 0. With probability p, a fill occurs and the size is exponentially distributed with rate . The empirical mean fill size is 2 and the empirical variance is 12. Use the method of moments to estimate p and .统计困难derivation未尝试面试订阅1726Design Effect Under Clustered AssignmentAn experiment randomizes by store rather than by customer. If the average cluster size is m and the intra-cluster correlation is , what is the standard design-effect multiplier on variance?统计中等derivation未尝试面试订阅1727Effective Sample Size After a CUPED-Style Variance ReductionA variance-reduction method shrinks the variance of the treatment-effect estimator by a factor of c where 0<c<1. By what factor does the effective sample size increase?统计中等derivation未尝试面试订阅1728Triggered Analysis Exposure FractionOnly a fraction q of randomized users ever encounter the feature being tested. If the treatment effect exists only on those triggered users, how does the intent-to-treat effect compare with the triggered-user effect?统计中等derivation未尝试面试订阅1729Why Session-Level Randomization Can Leak Across UsersWhy can session-level randomization be misleading when the same user returns many times and behavior carries over across sessions?统计简单essay未尝试免费1730Why Daily Peeking Breaks a Fixed-Horizon ThresholdWhy does checking significance every day against an unadjusted fixed-horizon p-value threshold inflate false positives?统计中等essay未尝试面试订阅1731Why Triggered Analysis Can Beat a Naive Population AverageWhy can triggered analysis produce a cleaner estimate than averaging over all randomized users?统计简单essay未尝试免费1732Why Interference Can Ruin User-Level RandomizationWhy can an experiment on social or marketplace features violate the usual randomized-test logic even if assignment itself was truly random?统计简单essay未尝试免费1733Why Guardrail Metrics Matter Even When the Primary Metric WinsWhy is a primary-metric win not enough to ship an experiment if latency, complaints, or cancellation rates deteriorate?统计中等essay未尝试面试订阅1734Why Novelty Effects Can Fake a Long-Run WinWhy can a treatment look great in the first week of an experiment and disappoint later even if the implementation is correct?统计简单essay未尝试免费1735Why Ratio Metrics Need More Care Than CountsWhy do ratio metrics such as revenue per active user often require more design care than simple counts?统计中等essay未尝试面试订阅1736Why Small p-Values Still Need a Plausible Rollout StoryWhy should a team still ask whether an observed experiment win makes operational sense even when the p-value is tiny?统计中等essay未尝试面试订阅1737Why Blocking on Seasonality Can Beat Pure RandomizationWhy can blocking by weekday, region, or season reduce noise in an experiment even though randomization alone is already unbiased?统计简单essay未尝试免费1738Why Cluster Tests Need More Than a Big User CountWhy can an experiment with millions of users still have weak power if it randomizes only a small number of clusters?统计中等essay未尝试面试订阅1739Why a Short Experiment Can Misread a Delayed EffectWhy can an experiment that ends too early miss a treatment whose benefits arrive only after a usage-learning period?统计简单essay未尝试免费1740Why Switchback Tests Help With Time-Based SpilloversWhy can alternating treatment and control by time block be more credible than user-level randomization when the whole marketplace state carries over across nearby minutes?统计中等essay未尝试面试订阅1778Lasso Threshold Calibration 3In an orthonormal lasso update, a coordinate has score z = 2.6 and penalty lambda = 1.1. What coefficient results after soft-thresholding?统计中等数值题未尝试免费1790Ridge Effective Degrees of Freedom 5A standardized ridge model has singular-value squares d j 2 = [12.25, 4, 0.25] and penalty lambda = 0.25. What is the effective degrees of freedom tr(S lambda) = sum d j 2/(d j 2+lambda)?统计困难derivation未尝试面试订阅1800Signal Stationarity Classification 5A candidate signal is defined by X t = t ε t. Is it weakly stationary?统计困难derivation未尝试面试订阅1815Validity or Stationarity Check 5Consider the proposal An MA(1) claiming rho(1)=0.7. Is it valid from a stationarity / autocorrelation perspective?统计困难数值题未尝试面试订阅