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1833MA(1) Invertibility Check 3An MA(1) execution-noise model uses theta = -0.7. Is the model invertible?统计中等数值题未尝试面试订阅1836AR(1) Forecast Error Variance 1For the AR(1) model X t = phi X (t-1) + e t with phi = 0.6 and Var(e t) = 1, what is the h = 3 step forecast error variance?统计简单derivation未尝试免费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1841ARMA Identification or Simplification 1You observe the diagnostic statement: ACF tails off geometrically, PACF cuts after lag 1. What is the correct modeling conclusion?统计简单数值题未尝试免费1842ARMA Identification or Simplification 2You observe the diagnostic statement: ACF cuts after lag 1, PACF tails off. What is the correct modeling conclusion?统计中等derivation未尝试面试订阅1844ARMA Identification or Simplification 4You observe the diagnostic statement: AIC prefers ARMA(2,1) but BIC prefers ARMA(1,1). What is the correct modeling conclusion?统计简单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1851Cumulative Mean-Reversion Carry 1A desk is short a positive residual and books one unit of carry each day equal to that day's expected residual. If X (t+1) = 3/4 X t + epsilon (t+1) with zero-mean shocks and X 0 = 12 bp, what is the total expected carry over the next 3 days?统计简单essay未尝试免费1856Horizon Risk Budget Ratio 1A stationary mean-reverting spread obeys X (t+1) = 1/2 X t + epsilon (t+1), where Var(epsilon (t+1)) = 4. Starting from the current level, what fraction of the same-horizon random-walk forecast-error variance does the 4-step mean-reverting forecast-error variance represent?统计简单derivation未尝试免费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1866RW Versus MR Diagnosis 1A residual's variance keeps growing roughly linearly with horizon and never appears to plateau. Which description fits better: random walk or mean reversion?统计简单essay未尝试免费1867RW Versus MR Diagnosis 2After a 10 bp shock, the expected residual is only 2 bp four days later. Does that behavior point more toward random walk or mean reversion?统计简单数值题未尝试免费1868RW Versus MR Diagnosis 3A five-day variance ratio comes in well below 1. What does that suggest about serial dependence in returns?统计中等essay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1874Original Launch Ratio from Differential SurvivalToday’s database contains 28 live discretionary funds and 42 live systematic funds. Historical survival rates were 40% for discretionary funds and 70% for systematic funds. What was the original launch ratio of discretionary funds to systematic funds?统计简单essay未尝试面试订阅1875Regional Launch Share ReconstructionA current hedge-fund database shows 36 live Asia funds and 24 live Europe funds. Historical survival rates were 60% for Asia funds and 80% for Europe funds. What fraction of the original launches were Asia funds?统计简单essay未尝试面试订阅1876Track-Record Age Bias 1As of end-2026, a database contains 45 surviving funds launched in 2024, 20 surviving funds launched in 2022, and 9 surviving funds launched in 2020. The corresponding survival rates were 90%, 50%, and 30%. By how many years does the average age in the live panel understate the average age across all original launches?统计中等essay未尝试面试订阅1877Track-Record Age Bias 2At end-2027, a manager database contains 54 surviving funds launched in 2026, 24 surviving funds launched in 2024, and 10 surviving funds launched in 2022. The survival rates for those vintages were 90%, 60%, and 40%. How many years does the live-panel average age understate the average age across all original launches?统计中等essay未尝试免费1878Track-Record Age Bias 3As of end-2028, a database shows 24 live funds launched in 2020 and 28 live funds launched in 2026. The survival rates for those two vintages were 40% and 80%, respectively. By how many years does the live-panel average age understate the true launch-universe average age?统计中等essay未尝试免费1879Full-Universe Average Launch YearAt end-2026, a live panel contains 18 funds launched in 2017 and 24 funds launched in 2021. The survival rates for those vintages were 30% and 80%, respectively. What was the average launch year across all original launches?统计中等essay未尝试面试订阅