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3500Covariance of W_2 + W_5 With W_4 - W_1What is Cov(W 2 + W 5, W 4 - W 1)?随机过程简单derivation未尝试面试订阅3501Conditional Mean of W_1 Given W_4 = 2Given W 4 = 2, what is E[W 1 | W 4 = 2]?随机过程简单derivation未尝试面试订阅3502Conditional Variance of W_1 Given W_4What is Var(W 1 | W 4)?随机过程简单derivation未尝试面试订阅3504Conditional Mean of W_2 + W_4 Given W_6 = 3Given W 6 = 3, what is E[W 2 + W 4 | W 6 = 3]?随机过程简单derivation未尝试面试订阅3505Conditional Mean of W_2 - W_1 Given W_5 = 1Given W 5 = 1, what is E[W 2 - W 1 | W 5 = 1]?随机过程简单derivation未尝试面试订阅3506Scaling Constant for a Unit-Variance IncrementChoose c so that c(W 9 - W 4) has variance 1.随机过程中等derivation未尝试面试订阅3507Tail Probability of a Four-Unit IncrementWhat is P(W 9 - W 5 > 2)?随机过程中等derivation未尝试面试订阅3508Time Needed for an Increment Variance of SixFind t such that Var(W t - W 1) = 6.随机过程中等derivation未尝试面试订阅3509Scale Factor Making W_8 / d Look Like W_2Choose d so that W 8 / d has the same distribution as W 2.随机过程中等derivation未尝试面试订阅3510Variance of a Rescaled Brownian Process at t = 3Define B t = W 4t / 2. What is Var(B 3)?随机过程中等derivation未尝试面试订阅3511Why Zero Covariance Gives Independence HereWhy does making two Brownian linear combinations uncorrelated automatically make them independent in these questions?随机过程中等essay未尝试面试订阅3512Why Brownian Scaling Is Operationally UsefulWhy is Brownian scaling more than a formal symmetry and actually useful in interview-style calculations?随机过程中等essay未尝试面试订阅3513Why Conditioning on an Endpoint Creates a BridgeWhy does conditioning Brownian motion on a future endpoint naturally produce bridge-style residuals?随机过程中等essay未尝试面试订阅3514Why Independent Increments Matter in Quant PracticeWhy is the independent-increment property operationally important when reasoning about multi-horizon risk or signal aggregation?随机过程中等essay未尝试面试订阅3515Why Brownian Paths Feel Smooth but Are NotWhy can Brownian paths be continuous everywhere and still fail to behave like ordinary smooth curves?随机过程中等essay未尝试面试订阅3516Touch Probability for Barrier 1 Over Horizon 1For standard Brownian motion, what is P(max 0<=s<=1 W s >= 1)?随机过程中等derivation未尝试面试订阅3518Barrier Giving Touch Probability 0.1 Over Horizon 9For standard Brownian motion over horizon t = 9, what barrier a gives touch probability 0.1?随机过程中等derivation未尝试面试订阅3519Barrier Giving Touch Probability 0.02 Over Horizon 0.25For standard Brownian motion over horizon t = 0.25, what barrier a gives touch probability 0.02?随机过程中等derivation未尝试面试订阅3520Horizon Needed for Touch Risk 0.2 Under Barrier 2For standard Brownian motion, what horizon t gives touch probability P(M t >= 2) = 0.2?随机过程中等derivation未尝试面试订阅3521Horizon Needed for Touch Risk 0.05 Under Barrier 1.8For standard Brownian motion, what horizon t gives touch probability P(M t >= 1.8) = 0.05?随机过程中等derivation未尝试面试订阅