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1498Exponential Tail Integral 3Evaluate integral 0 inf x e (-3x) dx.数学中等derivation未尝试免费1499Exponential Tail Integral 4Evaluate integral 0 inf x 2 e (-2x) dx.数学中等derivation未尝试免费1512Cross-Asset Log Ratio Curvature 2Compute the x 2 coefficient in ln(1+4x) - ln(1+-1x) - (5)x.数学简单数值题未尝试免费1518Skewed Ratio Approximation 3Use a second-order Taylor approximation around 0 to estimate (1+4x) (-1) * (1+-2x) (1/2) at x=1/25.数学中等derivation未尝试免费1521Quadratic Stress Calibration 1Choose c so that exp(2x + c x 2) - 1 - 2x has quadratic coefficient 5.数学简单数值题未尝试免费1633Two-Rate Latency Mixture With Known Mixing WeightA latency variable is a 50-50 mixture of two exponential laws with rates \lambda 1 and \lambda 2. The first two raw moments are m 1 and m 2. Write the two equations that method of moments imposes on (\lambda 1,\lambda 2).统计中等derivation未尝试面试订阅1797Signal Stationarity Classification 2A candidate signal is defined by X t = 0.2 t + ε t. Is it weakly stationary?统计中等derivation未尝试免费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1803Measurement Noise Effect 3A latent stationary signal Y t has gamma(0) = 6 and gamma(1) = -1. You observe X t = Y t + eta t, where eta t is iid noise with variance 4 independent of Y t. What are gamma X(0) and gamma X(1)?统计中等derivation未尝试免费1808Two-Point Sample Mean Variance 3A weakly stationary process has gamma(0) = 5 and gamma(1) = -1. What is Var((X 1 + X 2)/2)?统计中等数值题未尝试免费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1846Residual After 2 Rebalances 1A residual spread follows X (t+1) = 2/3 X t + epsilon (t+1) with E[epsilon (t+1)] = 0. If today's residual is 9 bp, what is E[X 2 | X 0 = 9 bp]?统计简单derivation未尝试免费1869RW Versus MR Diagnosis 4If a spread's conditional mean always equals today's level, regardless of horizon, which model is the closer description?统计中等derivation未尝试面试订阅1870RW Versus MR Diagnosis 5A desk notices that expected residual carry from holding a spread for longer horizons quickly saturates instead of growing linearly forever. Is that more consistent with random walk or mean reversion?统计困难derivation未尝试面试订阅1902Vendor Lag Alignment 2A vendor distributes a dataset with a fixed 3-business-day lag. If your model key is the Monday file and you trade at the open, what is the first valid trading session that may use that observation?统计中等derivation未尝试免费1921Required Observation Count 1A research lead uses the approximation n >= K * sigma 2 / delta 2 with K = 7.84, signal standard deviation 24 bp, and target detectable mean shift 3 bp. What is the minimum integer sample size?统计简单数值题未尝试免费1923Required Observation Count 3A research lead uses the approximation n >= K * sigma 2 / delta 2 with K = 9, signal standard deviation 30 bp, and target detectable mean shift 4 bp. What is the minimum integer sample size?统计中等数值题未尝试免费1928Minimum Detectable Edge 3Using the same approximation n >= K * sigma 2 / delta 2, suppose K = 9, sigma = 30 bp, and you can collect only n = 900 observations. What is the smallest detectable mean edge delta, in basis points?统计中等数值题未尝试免费