第 78 / 79 页
非代码面试题
显示 20 / 1576 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
5987When the Stopping Rule Looks at the Last DrawDraw i.i.d. values X 1,X 2,\dots uniform on \ 1,2,3\ (so E[X i]=2). Define N as follows: keep drawing and stop the first time you draw a 3; let N be the number of draws. Let S N=\sum i=1 N X i. A candidate computes E[N]E[X 1]=3 2=6 and claims E[S N]=6. Compute the correct value of E[S N] and explain in one sentence why E[N]E[X 1] is the wrong formula here.概率困难essay未尝试面试订阅6007Buys Before the First SellBuy fills and sell fills arrive as independent Poisson processes with rates \lambda 1=12 and \lambda 2=3 per hour. Counting from now, what is the expected number of buy fills that occur strictly before the first sell fill?概率中等derivation未尝试面试订阅6008Which of Three Feeds Ticks FirstThree independent market-data feeds emit ticks as Poisson processes with rates 5, 8, and 2 ticks per second. What is the probability that the very next tick across all feeds comes from the rate-8 feed?概率简单derivation未尝试面试订阅6009Expected Large Trades in Two HoursTrades print as a Poisson process at rate =30 per hour. Independently, each trade is a block (large) trade with probability 0.15. What is the expected number of block trades over the next 2 hours?概率简单derivation未尝试面试订阅6010No Orders Routed to Venue COrders arrive as a Poisson process at rate =20 per minute and are independently routed to venue A, B, or C with probabilities 0.5, 0.25, and 0.25. What is the probability that venue C receives no orders during the next 6 seconds?概率中等derivation未尝试面试订阅6011Joint Count of Two Split StreamsA Poisson process at rate =30 per hour is split by independent fair-coin-style labeling into a 'lit' stream (prob 0.2) and a 'dark' stream (prob 0.8). Over the next 30 minutes, what is the probability of observing exactly 4 lit prints and exactly 9 dark prints?概率中等derivation未尝试面试订阅6012A Three-Arrival Head StartAggressive and passive child orders fill as independent Poisson processes with rates \lambda A=10 and \lambda B=5 per minute. What is the probability that the first three fills in the merged stream are all aggressive (stream A)?概率简单derivation未尝试面试订阅6016Posterior Mean Hit Rate After a Cold StreakA signal's hit probability p has prior Beta (4,4). Over the next batch you record 3 hits and 9 misses. By integrating the posterior density, what is the posterior mean of p?统计简单derivation未尝试免费6018Posterior Mean Rate for a Rare FaultFaults arrive as a Poisson process with rate per day, prior Gamma (2,0.5) in shape-rate form. Over 3.5 days you observe 7 faults. What is the posterior mean of ?统计中等derivation未尝试免费6020Predictive Chance the Next Trade FailsA fill probability p has prior Beta (2,1). After observing 3 fills and 4 misses, what is the posterior predictive probability that the very next attempt is a miss (a failure)?统计中等derivation未尝试免费6023Long-Run Volatility (Not Variance) from GARCH ParametersA GARCH(1,1) model h t=\omega+ r t-1 2+ h t-1 has \omega=0.04, =0.12, =0.80. Here h t is the conditional variance of daily returns. Report the long-run (unconditional) daily volatility h as a decimal.统计中等derivation未尝试面试订阅6024Persistence and the Covariance-Stationarity VerdictA GARCH(1,1) has =0.20, =0.75. Compute the persistence + and state whether the process is covariance-stationary (i.e. has a finite, time-invariant unconditional variance). Give the persistence as a decimal.统计简单derivation未尝试面试订阅6025Five-Step Forecast via the Mean-Reversion FormulaFor a GARCH(1,1) with \omega=0.2, =0.1, =0.8, the one-step-ahead conditional variance is h t+1 =3. Using the closed form E t[h t+k ]= h+( + ) \,k-1 (h t+1 - h), compute the 5-step-ahead forecast E t[h t+5 ] as a decimal.统计困难derivation未尝试面试订阅6026ARCH(1) as the Beta-Zero Special CaseA GARCH(1,1) reduces to ARCH(1) when =0: h t=\omega+ r t-1 2. With \omega=0.7 and =0.3, compute the unconditional variance h as a decimal.统计简单derivation未尝试面试订阅6027When GARCH(1,1) Becomes EWMARiskMetrics EWMA updates variance as h t=(1- )r t-1 2+ h t-1 . State the constraints on (\omega, , ) that make GARCH(1,1) coincide exactly with EWMA, and give the implied when =0.06. Report as a decimal.统计中等数值题未尝试面试订阅6028Fat Tails: Unconditional Kurtosis of GARCH ReturnsLet r t= h t \,z t with z t\sim N(0,1) i.i.d. and GARCH(1,1) variance. The unconditional kurtosis (when finite) is K=\dfrac 3\,[1-( + ) 2] 1-( + ) 2-2 2 . For =0.1, =0.85, compute K and state whether returns are leptokurtic. Give K as a decimal.统计困难derivation未尝试面试订阅6029News-Impact Update from a Signed ReturnA GARCH(1,1) has \omega=0.00001, =0.08, =0.90. Today's conditional variance is h t=0.0004 and today's return is r t=-0.03. Compute tomorrow's conditional variance h t+1 as a decimal.统计中等derivation未尝试面试订阅6030One-Step Prediction with a Persistence CoefficientA latent state evolves as x t=0.9\,x t-1 +w t with w t\sim N(0,2). At time t-1 the filtered state is N(4,3). Compute the one-step-ahead predicted mean and predicted variance of x t (before any observation at time t).统计简单derivation未尝试免费6031Kalman Gain AloneIn a scalar measurement update y=x+\varepsilon with \varepsilon\sim N(0,4), the prior (predicted) state variance is P -=12. What fraction of the innovation is incorporated into the updated estimate, i.e. compute the Kalman gain K.统计简单数值题未尝试免费6032How Much Does One Print Shrink Uncertainty?A predicted state has variance P -=10. A single observation arrives with noise variance R=6 in the model y=x+\varepsilon. By how much does the posterior (updated) variance fall below P -? Give the updated variance P +.统计简单数值题未尝试免费