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3618Quadratic Variation of 0.5W_t Plus an Integrated DriftLet X t = 0.5W t + integral 0 t s ds. What is [X] 4?随机过程中等derivation未尝试面试订阅3619Quadratic Variation of Brownian Motion with Two Smooth CorrectionsLet X t = W t - t + cos t. What is [X] 3?随机过程中等derivation未尝试面试订阅3620Quadratic Variation of 1.2W_t Plus a Rational DriftLet X t = 1.2W t + t/(1+t). What is [X] 5?随机过程中等derivation未尝试面试订阅3621Quadratic Variation of an Itô Integral with Linear LoadingLet X t = integral 0 t (1+s) dW s. What is [X] 2?随机过程中等derivation未尝试面试订阅3622Quadratic Variation of an Itô Integral with Descending LoadingLet X t = integral 0 t (2-s) dW s. What is [X] 1?随机过程中等derivation未尝试面试订阅3623Quadratic Variation of a Piecewise-Volatility IntegralLet X t = integral 0 t sigma(s) dW s where sigma(s)=1 on [0,1], sigma(s)=2 on (1,2], and sigma(s)=0 on (2,3]. What is [X] 3?随机过程中等derivation未尝试面试订阅3624Quadratic Variation of a Square-Root LoadingLet X t = integral 0 t sqrt(1+s) dW s. What is [X] 3?随机过程中等derivation未尝试面试订阅3625Quadratic Variation of a Rescaled Time Polynomial LoadingLet X t = integral 0 t (s/3) dW s. What is [X] 3?随机过程中等derivation未尝试面试订阅3626Covariation of W_t+2B_t with 3W_t-B_tLet X t = W t + 2B t and Y t = 3W t - B t where W and B are independent Brownian motions. What is [X,Y] 1?随机过程中等derivation未尝试面试订阅3627Covariation of 2W_t-B_t with W_t+4B_tLet X t = 2W t - B t and Y t = W t + 4B t with independent W and B. What is [X,Y] 2?随机过程中等derivation未尝试面试订阅3628Covariation of 0.5W_t+B_t with 3W_t+2B_tLet X t = 0.5W t + B t and Y t = 3W t + 2B t with independent W and B. What is [X,Y] 4?随机过程中等derivation未尝试面试订阅3629Covariation of W_t-B_t with W_t+B_tLet X t = W t - B t and Y t = W t + B t with independent W and B. What is [X,Y] 3?随机过程中等derivation未尝试面试订阅3630Covariation of 2W_t+3B_t with -W_t+2B_tLet X t = 2W t + 3B t and Y t = -W t + 2B t with independent W and B. What is [X,Y] 0.5 ?随机过程中等derivation未尝试面试订阅3631Coefficient Making [W_t+aB_t]_2 Equal 10Choose a so that [W t + aB t] 2 = 10 where W and B are independent Brownian motions.随机过程中等derivation未尝试面试订阅3632Coefficient Making [W_t+aB_t, 2W_t-B_t]_1 Equal ZeroChoose a so that [W t + aB t, 2W t - B t] 1 = 0 with independent W and B.随机过程中等derivation未尝试面试订阅3633Scale Making [cW_{4t}]_1 Equal 1Choose c so that [cW 4t ] 1 = 1.随机过程中等derivation未尝试面试订阅3634Coefficient Making [aW_t+B_t]_3 Equal 15Choose a so that [aW t + B t] 3 = 15 with independent W and B.随机过程中等derivation未尝试面试订阅3635Coefficient Making [aW_t-B_t, W_t+B_t]_2 Equal 6Choose a so that [aW t - B t, W t + B t] 2 = 6 with independent W and B.随机过程中等derivation未尝试面试订阅3636Why Smooth Drift Terms Disappear from Quadratic VariationWhy do smooth finite-variation terms fail to contribute to quadratic variation even though they can dominate the path in level?随机过程中等essay未尝试面试订阅3637Why Independent Brownian Motions Have Zero CovariationWhy does independence of Brownian drivers force the covariation term to vanish?随机过程中等essay未尝试面试订阅