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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4926Infer One-Day VaR From Multi-Day Scaling 11Under square-root-of-time Gaussian scaling, a 10-day VaR is 7.589466. What 1-day VaR does that imply?数理金融中等数值题未尝试面试订阅4928Infer Pareto Tail Index From ES To VaR Ratio 13For a Pareto tail, suppose ES/VaR = alpha/(alpha-1). If VaR is 8 and ES is 12, what tail index alpha is implied?数理金融中等数值题未尝试面试订阅4929Infer Pareto Tail Index From ES To VaR Ratio 14For a Pareto tail with ES/VaR = alpha/(alpha-1), if VaR is 5.5 and ES is 9.166667, what alpha is implied?数理金融中等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4951Infer Domain Length From First Dirichlet Eigenvalue 11For y'' + lambda y = 0 on [0,L] with y(0)=0 and y(L)=0, the first positive eigenvalue is lambda 1 = (pi/L) 2. If lambda 1 = 4*pi 2, what is L?数学中等数值题未尝试面试订阅4952Infer Domain Length From First Dirichlet Eigenvalue 12For y'' + lambda y = 0 on [0,L] with Dirichlet endpoints, the first positive eigenvalue is lambda 1 = (pi/L) 2. If lambda 1 = pi 2/4, what is L?数学中等数值题未尝试面试订阅4953Boundary Eigenvalue 3For y'' + λ y = 0 on [0,1] with y'(0)=0 and y(1)=0, what is the 1-th positive eigenvalue?数学中等数值题未尝试面试订阅4954Boundary Eigenvalue 4For y'' + λ y = 0 on [0,1.5] with y(0)=0 and y(1.5)=0, what is the 2-th positive eigenvalue?数学中等数值题未尝试面试订阅4956Infer Poisson Forcing From Arc Maximum 13Let y solve y'' = -c on [0,1] with y(0)=0 and y(1)=0. If the maximum value of y on the interval is 0.25, what c is implied?数学中等数值题未尝试面试订阅