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3483Expected Questions With a Rare-State TailA binary tree uses code lengths [2, 2, 2, 3, 3] for states with priors [1/4, 1/4, 1/4, 1/8, 1/8]. What is the expected number of questions?数学中等derivation未尝试面试订阅3484Expected Questions Under a Heavy First StateA binary tree uses code lengths [1, 3, 3, 3, 3] for priors [1/2, 1/8, 1/8, 1/8, 1/8]. What is the expected number of questions?数学中等derivation未尝试面试订阅3485Expected Questions in a Ternary-Then-Binary StrategyA strategy first asks a ternary question that isolates state A on one branch, state B on another branch, and groups states C and D on the last branch. If the prior over [A, B, C, D] is [0.4, 0.3, 0.2, 0.1], what is the expected number of questions if the grouped branch uses one extra yes/no question?数学中等derivation未尝试面试订阅3486Why Adaptive Testing Beats Static MenusWhy can an adaptive questioning strategy distinguish more states than a non-adaptive test battery with the same primitive tests?数学中等essay未尝试面试订阅3487Why Entropy Is a Lower Bound, Not Always an Exact CountWhy does the Shannon entropy of the prior give only a lower bound on expected yes/no questions rather than always the exact optimum?数学中等essay未尝试面试订阅3488Why a None State Changes the Coding ProblemIn one-defective search problems, why does adding the possibility of no defect change the counting argument in a substantive way?数学中等essay未尝试面试订阅3489Why Prior Skew Should Change the Query TreeWhy should the optimal query tree usually isolate high-probability states earlier than low-probability states?数学中等essay未尝试面试订阅3490Why Branch Constraints Can Matter More Than Alphabet SizeWhy can two testing systems with the same maximum branch count per question have very different identification power once branch-specific follow-up rules are imposed?数学中等essay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