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1439Logarithmic Sequence CorrectionCompute lim n->∞ n 2 [ln(1+1/n) - 1/n].数学困难数值题未尝试面试订阅1444Trigonometric Asymptotic 4Compute lim (x->0) [arctan(5x) - 5x] / x 3.数学困难数值题未尝试面试订阅1450Mixed-Expansion Limit 5Compute lim (x->0) [ln(cosh(2x))] / x 2.数学困难数值题未尝试面试订阅1527Stress-Adjusted Determinant 2An invertible matrix A has det(A) = 5. For vectors u and v, suppose v T A (-1) u = -3/5. What is det(A + u v T)?数学简单数值题未尝试免费1545Sherman-Morrison Failure TestWhy does the Sherman-Morrison formula break down exactly when 1 + v T A (-1)u = 0?数学困难数值题未尝试面试订阅1615Signed-Factor Covariance Entry 2Under a one-factor model X = bF + epsilon with factor variance 5, asset loadings (2, -1), and idiosyncratic variances (1, 4), what are Var(X 1), Var(X 2), and Cov(X 1, X 2)?数学困难derivation未尝试面试订阅1619Why Large Condition Number Destabilizes WeightsWhy does a covariance matrix with a very large condition number make optimized portfolio weights unstable?数学困难essay未尝试面试订阅1776Lasso Threshold Calibration 1A standardized lasso fit has score vector (4.1, 2.3, 1.7). What is the smallest lambda that makes every coefficient exactly zero?统计中等derivation未尝试免费1779Lasso Threshold Calibration 4In an orthonormal lasso update, a coordinate has score z = -3.2 and penalty lambda = 0.7. What coefficient results after soft-thresholding?统计中等derivation未尝试免费1780Lasso Threshold Calibration 5A standardized lasso model has absolute scores (5.0, 4.0, 1.5). What is the smallest lambda that leaves only the strongest feature nonzero?统计困难derivation未尝试免费1787Ridge Effective Degrees of Freedom 2A standardized ridge model has singular-value squares d j 2 = [16, 4] and penalty lambda = 4. What is the effective degrees of freedom tr(S lambda) = sum d j 2/(d j 2+lambda)?统计中等derivation未尝试免费1795Why the One-SE Rule Is ConservativeWhy do practitioners often prefer the one-standard-error rule over the absolute CV minimizer when selecting a regularization parameter?统计困难essay未尝试面试订阅1798Signal Stationarity Classification 3A candidate signal is defined by X t = ε t + s t where s t is a fixed deterministic day-of-week pattern. Is it weakly stationary?统计简单derivation未尝试免费1812Validity or Stationarity Check 2Consider the proposal rho(1)=1.2. Is it valid from a stationarity / autocorrelation perspective?统计中等derivation未尝试免费1813Validity or Stationarity Check 3Consider the proposal An AR(1) with phi = 1.03. Is it valid from a stationarity / autocorrelation perspective?统计中等数值题未尝试免费1814Validity or Stationarity Check 4Consider the proposal An AR(1) with phi = -0.6. Is it valid from a stationarity / autocorrelation perspective?统计困难derivation未尝试面试订阅1818Why Ergodicity MattersWhy is ergodicity stronger than stationarity, and why do practitioners care about it when they average one long signal history?统计中等derivation未尝试免费1820Measurement Noise Flattens ACFWhy can adding independent observation noise make an otherwise persistent signal look less autocorrelated?统计困难derivation未尝试面试订阅1838AR(1) Forecast Error Variance 3For the AR(1) model X t = phi X (t-1) + e t with phi = 0.5 and Var(e t) = 2.25, what is the h = 4 step forecast error variance?统计中等essay未尝试面试订阅1861Long-Run Residual Variance 1A mean-reverting residual follows X (t+1) = 1/2 X t + epsilon (t+1) with Var(epsilon (t+1)) = 4. What is the stationary variance of X t?统计简单essay未尝试免费