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4918Infer Normal Parameters From VaR And ES 3A risk report uses alpha=0.975 with z=1.96 and k=2.338 in the formulas VaR = mu + z*sigma and ES = mu + k*sigma. If VaR is 11.8 and ES is 13.69, what are mu and sigma?数理金融中等数值题未尝试面试订阅4919Infer Normal Parameters From VaR And ES 4A normal-loss desk uses alpha=0.95 with z=1.645 and k=2.063. If the reported VaR is 4.1125 and ES is 5.1575, what are mu and sigma?数理金融中等数值题未尝试面试订阅4920Infer Normal Parameters From VaR And ES 5A desk uses alpha=0.99 with z=2.326 and k=2.665 in the formulas VaR = mu + z*sigma and ES = mu + k*sigma. If VaR is 15.156 and ES is 17.19, what are mu and sigma?数理金融中等数值题未尝试面试订阅4921Infer Missing Tail Observation 6Sorted empirical losses are [1, 2, 3, 4, 7, 9, 12, x]. Using alpha=0.75, define empirical VaR as the ceil(alpha*n)-th order statistic and empirical ES as the average of losses at and beyond that cutoff. If empirical ES is 11.5, what is x?数理金融中等数值题未尝试面试订阅4922Infer Missing Tail Observation 7Sorted empirical losses are [0, 1, 1, 3, 5, 6, 8, x]. Using alpha=0.875 with the same empirical VaR and ES conventions, if empirical ES is 9.5, what is x?数理金融中等数值题未尝试面试订阅4923Infer Missing Tail Observation 8Sorted empirical losses are [2, 2, 4, 5, 7, 10, 13, x]. Using alpha=0.75 and the same conventions, if empirical ES is 15, what is x?数理金融中等数值题未尝试面试订阅4924Infer Missing Tail Observation 9Sorted empirical losses are [1, 1, 2, 4, 4, 7, 9, x]. Using alpha=0.875 and the same conventions, if empirical ES is 11.5, what is x?数理金融中等数值题未尝试面试订阅4931Infer Portfolio Covariance Loading From Component VaR 16For a linear Gaussian portfolio, component VaR satisfies component i = w i * z alpha * (Sigma w) i / sigma p. If z alpha=1.645, sigma p=0.2, w i=0.6, and the reported component VaR is 0.11844, what covariance loading (Sigma w) i is implied?数理金融困难数值题未尝试面试订阅4932Infer Portfolio Covariance Loading From Component VaR 17For a linear Gaussian portfolio, z alpha=2.326, sigma p=0.3, w i=0.35, and the reported component VaR is 0.111260333. What covariance loading (Sigma w) i is implied?数理金融困难数值题未尝试面试订阅4933Infer Portfolio Covariance Loading From Component VaR 18For a linear Gaussian portfolio, z alpha=1.96, sigma p=0.25, w i=0.5, and the component VaR is 0.1176. What covariance loading (Sigma w) i is implied?数理金融困难数值题未尝试面试订阅4941Infer Constant Forcing From Midpoint 1Let y solve y'' = c on [0,1] with y(0)=0 and y(1)=3. If y(1/2)=1.25, what constant c is implied?数学简单数值题未尝试面试订阅4942Infer Constant Forcing From Midpoint 2Let y solve y'' = c on [0,1] with y(0)=1 and y(1)=2. If y(1/2)=2, what c is implied?数学简单数值题未尝试面试订阅4943Infer Constant Forcing From Midpoint 3Let y solve y'' = c on [0,1] with y(0)=-1 and y(1)=1. If y(1/2)=-0.75, what c is implied?数学简单数值题未尝试面试订阅4944Infer Constant Forcing From Midpoint 4Let y solve y'' = c on [0,1] with y(0)=2 and y(1)=4. If y(1/2)=2.8125, what c is implied?数学简单数值题未尝试面试订阅4945Infer Constant Forcing From Midpoint 5Let y solve y'' = c on [0,1] with y(0)=0.5 and y(1)=1.5. If y(1/2)=1.25, what c is implied?数学简单数值题未尝试面试订阅4946Infer Interval Length From Mixed Boundary Data 6Let y solve y''=0 on [0,L] with y(0)=1 and y'(0)=2. If y(L)=4, what interval length L is implied?数学简单数值题未尝试面试订阅4947Infer Interval Length From Mixed Boundary Data 7Let y solve y''=0 on [0,L] with y(0)=5 and y'(0)=-1.5. If y(L)=2, what L is implied?数学简单数值题未尝试面试订阅4948Infer Interval Length From Mixed Boundary Data 8Let y solve y''=0 on [0,L] with y(0)=2.2 and y'(0)=0.4. If y(L)=3.4, what L is implied?数学简单数值题未尝试面试订阅4949Infer Interval Length From Mixed Boundary Data 9Let y solve y''=0 on [0,L] with y(0)=-1 and y'(0)=1.2. If y(L)=2, what L is implied?数学简单数值题未尝试面试订阅4950Infer Interval Length From Mixed Boundary Data 10Let y solve y''=0 on [0,L] with y(0)=4.5 and y'(0)=-0.5. If y(L)=3.9, what L is implied?数学简单数值题未尝试面试订阅