第 24 / 88 页
非代码面试题
显示 20 / 1751 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
2719Why Parameter Stability Matters More Than the Single Best PeakWhy is a broad plateau of good parameter values often more convincing than one spectacularly sharp optimum in a backtest heatmap?机器学习中等essay未尝试面试订阅2720Why Live Degradation Should Be the Default ExpectationWhy should a PM expect live performance to come in below the very best backtest rather than treat any shortfall as an implementation surprise?机器学习困难essay未尝试面试订阅2724Recurrence Hidden in a Rational Generating FunctionLet A(x)=sum n>=0 a n x n = (1+x)/(1-2x+x 3). Derive a linear recurrence for a n and compute a 5.脑筋急转弯困难derivation未尝试面试订阅2729Chip Allocation With a Congruence ConstraintTwelve identical chips are allocated across four desks. How many allocations have the property that the combined chips on desks 1 and 2 are divisible by 3?脑筋急转弯困难derivation未尝试面试订阅2736A Fibonacci Binomial Sum From Coefficient ExtractionEvaluate sum k>=0 C(12-k, k). You should explain why a generating function turns this into a Fibonacci-type coefficient.脑筋急转弯中等derivation未尝试面试订阅2816PGF of a Binomial VariableLet X\sim Binomial (n,p). Derive its probability generating function G X(s) and use it to recover E[X].概率中等derivation未尝试面试订阅2817Sum of Independent Poisson CountsLet X\sim Poisson (\lambda 1) and Y\sim Poisson (\lambda 2) be independent. Use PGFs to identify the distribution of X+Y.概率中等derivation未尝试面试订阅2818Poisson ThinningSuppose N\sim Poisson ( ) and each event is independently kept with probability p. Let K be the number kept. Use PGFs to identify the law of K.概率中等derivation未尝试面试订阅2819A Generic Even-Parity FormulaLet X be a nonnegative integer-valued random variable with PGF G X(s). Express P(X is even ) in terms of G X(-1).概率中等derivation未尝试面试订阅2820Even Poisson CountIf N\sim Poisson ( ), use its PGF to compute P(N is even ).概率中等derivation未尝试面试订阅2821Even Binomial CountIf X\sim Binomial (n,p), compute P(X is even ) using the PGF.概率中等derivation未尝试面试订阅2822Extinction for Offspring 0 or 2A Galton-Watson branching process has offspring PGF \phi(s)=0.3+0.7s 2. Compute the extinction probability.概率中等derivation未尝试面试订阅2824Critical 0-or-2 BranchingA branching process has offspring PGF \phi(s)=\frac12+\frac12 s 2. What is the extinction probability?概率中等derivation未尝试面试订阅2825Compound Poisson With Geometric Batch SizeLet N\sim Poisson (2), and conditional on N, let \[ S=\sum i=1 N B i, \] where the B i are i.i.d. geometric-on-\ 1,2,\dots\ with parameter 1/2, so P(B i=k)=2 -k . Find the PGF of S and compute E[S].概率中等derivation未尝试面试订阅2827Generic Thinning of an Arbitrary CountLet X be a nonnegative integer-valued random variable with PGF G X(s). Each of the X items is independently kept with probability p. If Y is the number kept, express G Y(s) in terms of G X.概率中等derivation未尝试面试订阅2828Mean and Variance After ThinningUnder the thinning setup above, derive E[Y] and Var (Y) in terms of E[X] and Var (X).概率中等derivation未尝试面试订阅2829A Geometric Number of Bernoulli TrialsLet N have the geometric law on \ 0,1,2,\dots\ with P(N=n)=p(1-p) n. Conditional on N, let \[ S=\sum i=1 N X i, \] where the X i are i.i.d. Bernoulli(q). Find the PGF of S and identify its distribution.概率中等derivation未尝试面试订阅2830Total Progeny PGF EquationLet \phi(s) be the offspring PGF of a Galton-Watson branching process started from one ancestor, and let T be the total progeny. Show that the PGF of T satisfies \[ G T(s)=s\,\phi(G T(s)). \]概率中等derivation未尝试面试订阅2831Mean Total Progeny in the Subcritical CaseSuppose a Galton-Watson branching process starts from one ancestor and has offspring PGF \phi with mean m=\phi'(1)<1. Use the total-progeny PGF equation to derive E[T].概率中等derivation未尝试面试订阅2832Binomial Number of Trade BatchesLet N\sim Binomial (5,0.4). Conditional on N, let \[ S=\sum i=1 N B i, \] where each batch size B i has PGF H(s)=0.5+0.3s+0.2s 2. Find the PGF of S and compute E[S].概率中等derivation未尝试面试订阅