第 40 / 41 页
非代码面试题
显示 20 / 814 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
5979Three-Level Exit With a Non-Absorbing BarrierA fair simple random walk starts at 0. Three levels are marked: -3, +2, and +6. Only the two extreme levels, -3 and +6, are absorbing; the walk passes freely through +2. Find the probability the walk is absorbed at -3, and the expected absorption value E[S T].概率困难数值题未尝试面试订阅5980Random Walk With Rest PeriodsA process evolves in rounds. Each round, independently, with probability 1/2 the walker rests (position unchanged) and with probability 1/2 it takes a step that is +1 or -1 with equal odds. The walker stops at the first round in which it completes its 8th actual (non-rest) step. Let S be the position at that stopping time. Find E[S 2].概率中等数值题未尝试免费5981Total Stake Until the First SixYou roll a fair die repeatedly until the first time a 6 appears; let N be the number of rolls (including the winning roll). On each roll you independently collect a payoff X i with E[X i]=1.5, where the X i are i.i.d. and independent of the roll values. Compute E\! [\sum i=1 N X i ].概率简单derivation未尝试免费5982Variance of Fills Over a Binomial Number of QuotesOut of n=10 resting quotes, each fills independently with probability 0.3, so the number of fills N is Binomial(10,0.3). Each fill produces an i.i.d. PnL X i with E[X i]=2 and Var (X i)=9, independent of which quotes fill. For the stopped sum S N=\sum i=1 N X i, compute Var (S N).概率中等derivation未尝试免费5983Number of Trades to Cross a Profit TargetA strategy books i.i.d. positive profits X 1,X 2,\dots with E[X i]=2.5. Let N be the first time the running total S n=\sum i=1 n X i strictly exceeds 10; that is, N=\min\ n:S n>10\ . Assuming E[N]< , the expected overshoot is known to satisfy E[S N]=14. Use a Wald-style identity to compute E[N].概率中等derivation未尝试免费5984Expected Inspection Cost Until the First DefectA quality line inspects items one at a time; each item is defective independently with probability 0.05. Inspection stops at the first defective item. Each inspection (defective or not) costs an i.i.d. amount C i with E[C i]=\8, independent of the defect outcomes. Let N be the number of items inspected. Find the expected total inspection cost E\! [\sum i=1 N C i ].概率简单数值题未尝试免费5985Expected Total Slippage With Negative DriftA market-making desk incurs i.i.d. per-trade adverse-selection costs X 1,X 2,\dots with E[X i]=-0.4 (a net loss per trade). The number of trades in a session, N, is independent of the costs and is Poisson with mean 15. Compute the expected cumulative cost E\! [\sum i=1 N X i ].概率简单derivation未尝试免费5986Expected Winnings Over a Random Number of BetsA gambler places bets until a random stopping rule halts play; the number of bets N is a stopping time for the i.i.d. bet outcomes with E[N]=8. Each bet has an i.i.d. net result X i with E[X i]=-0.05 (a 5\% house edge per unit staked, with unit stakes), and the decision to stop after bet n depends only on outcomes up to bet n. Compute the gambler's expected total winnings E\! [\sum i=1 N X i ], and state whether any stopping rule with E[N]=8 can make this positive.概率中等derivation未尝试免费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5988Expected Sample Size of a Sequential Drift TestA sequential test accumulates i.i.d. log-likelihood increments X 1,X 2,\dots with E[X i]=0.25. The test stops at N=\min\ n: |S n|\ge 3\ where S n=\sum i=1 n X i, and it is given that E[N]< and that the expected stopped statistic is E[S N]=2.0 (reflecting that the upper boundary is hit far more often under this positive drift). Each observation costs \6 to collect. Using a Wald-style identity, find the expected total data-collection cost.概率中等数值题未尝试免费5989Variance of a Count WindowTrades hit a tape as a Poisson process with rate 6 per hour. Let N be the number of trades in a fixed 20-minute window. What is Var (N)?概率简单数值题未尝试免费5990Expected Time to the Third ArrivalOrders arrive at a matching engine as a Poisson process with rate 4 per minute. What is the expected time, in seconds, until the 3rd order arrives (measured from time 0)?概率简单数值题未尝试免费5991Quiet Window on a Combined FeedTwo independent exchanges send quotes to your gateway. Exchange A is a Poisson process with rate 3 per minute and exchange B is an independent Poisson process with rate 5 per minute. Treating the combined stream as one process, what is the probability that no quote arrives during a 30-second window? Give a decimal to three places.概率中等数值题未尝试免费5992Most Likely Number of FillsFills on a passive order arrive as a Poisson process with rate 7 per hour. Over a fixed 30-minute window, what is the single most likely number of fills (the mode of the count distribution)?概率中等数值题未尝试免费5993Waiting After a Quiet StretchCustomer arrivals at a help desk form a Poisson process with rate 12 per hour. You have already waited 2 minutes since the last arrival with no one appearing. What is the probability you must wait at least 5 more minutes for the next arrival? Give a decimal to three places.概率中等数值题未尝试免费5994At Least Two ArrivalsDefaults in a small credit book occur as a Poisson process with rate 8 per year. What is the probability that at least 2 defaults occur in the next 3 months? Give a decimal to three places.概率中等数值题未尝试免费5995Rate from a Mean GapTrades on an illiquid name arrive as a Poisson process. The average time between consecutive trades is observed to be 4 minutes. What is the implied arrival rate, expressed as trades per hour?概率简单数值题未尝试免费5996Variance of the Fourth Arrival TimePackets arrive at a sensor as a Poisson process with rate 2 per minute. Let T 4 be the time of the 4th packet. What is Var (T 4), in minutes squared?概率中等数值题未尝试免费5997Expected Count Under an Unknown RegimeOn any given day the market is in a 'calm' regime with probability 0.5, where news events arrive as a Poisson process with rate 6 per hour, or a 'busy' regime with probability 0.5, with rate 14 per hour. Before observing the day you do not know the regime. What is the expected number of news events in a 1-hour window?概率中等数值题未尝试免费5998First Arrival Lands in a Target WindowSignals arrive as a Poisson process with rate 1 per second. What is the probability that the very first signal arrives strictly between 2 and 3 seconds after the start? Give a decimal to three places.概率困难数值题未尝试免费