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2991Quiet Ten-Minute Window RateEvents follow a Poisson process with hourly rate . What value of makes the probability of zero events in the next 10 minutes exactly 0.7?概率简单derivation未尝试面试订阅2996First Arrival Before Market Open Plus Two MinutesMessages arrive as a Poisson process with rate 9 per hour. What is the probability the first arrival occurs within 2 minutes?概率中等derivation未尝试面试订阅3000First Order Before Twenty SecondsMessages arrive as a Poisson process with rate 45 per hour. What is the probability the first arrival occurs within 0.3333333333333333 minutes?概率中等derivation未尝试面试订阅3001Exactly One in the First Half Hour and None in the SecondA Poisson process has rate 8 per hour. What is the probability of exactly one arrival in the first 30 minutes and zero arrivals in the next 30 minutes?概率简单derivation未尝试面试订阅3002Two in the First Ten Minutes and Zero in the Next FiveA Poisson process has rate 24 per hour. What is the probability of exactly two arrivals in the first 10 minutes and zero arrivals in the next 5 minutes?概率简单derivation未尝试面试订阅3003No Messages Early but At Least One LaterA Poisson process has rate 15 per hour. What is the probability of zero arrivals in the first 4 minutes and at least one arrival in the next 8 minutes?概率简单derivation未尝试面试订阅3011Median Waiting Time for a One-Per-Hour FeedArrivals follow a Poisson process with rate 1 per hour. What is the median waiting time to the first arrival, in minutes?概率简单derivation未尝试面试订阅3016Buy Orders Beat Sell OrdersBuy orders and sell orders arrive as independent Poisson processes with rates \lambda A=7 and \lambda B=5 per hour. What is the probability that the next arrival in the merged stream comes from stream A?概率简单derivation未尝试面试订阅3017Exchange A Sends the Next Tick FirstExchange a ticks and Exchange B ticks arrive as independent Poisson processes with rates \lambda A=9 and \lambda B=3 per hour. What is the probability that the next arrival in the merged stream comes from stream A?概率简单derivation未尝试面试订阅3018Institutional RFQ Before Retail RFQInstitutional rfqs and retail RFQs arrive as independent Poisson processes with rates \lambda A=4 and \lambda B=6 per hour. What is the probability that the next arrival in the merged stream comes from stream A?概率简单derivation未尝试面试订阅3019Options Alarm Before Cash AlarmOptions alarms and cash alarms arrive as independent Poisson processes with rates \lambda A=8 and \lambda B=2 per hour. What is the probability that the next arrival in the merged stream comes from stream A?概率简单derivation未尝试面试订阅3020API Error Before Database ErrorApi errors and database errors arrive as independent Poisson processes with rates \lambda A=5 and \lambda B=5 per hour. What is the probability that the next arrival in the merged stream comes from stream A?概率简单derivation未尝试面试订阅3021Merged Count in 15 MinutesTwo independent Poisson streams with rates 6 and 10 per hour are merged. What is the probability that the merged stream records exactly 3 arrivals in the next 15 minutes?概率简单derivation未尝试面试订阅3026Buy Prints After ThinningEvents arrive as a Poisson process with rate =18 per hour. Each event is independently tagged as type A with probability 2 5 . What is the probability of exactly 2 type-A events in the next 20 minutes?概率中等derivation未尝试面试订阅3031How Many of Eight Merged Orders Came from Venue A?Two independent Poisson streams A and B with hourly rates 7 and 3 are merged. Conditional on observing exactly 8 merged arrivals in the hour, what is the probability that exactly 5 came from stream A?概率中等derivation未尝试面试订阅3036First Two Merged Arrivals Are Both BuysTwo independent Poisson streams with rates 8 and 4 per hour are merged. Using the fact that source labels in the merged stream are i.i.d., compute the requested probability about the first 2 merged arrivals.概率中等derivation未尝试面试订阅3041Expected First Arrival Given Four in an HourA Poisson process is observed on [0,1] hours. Conditional on exactly 4 arrivals in that horizon, what is the expected time of the 1-th arrival?概率中等derivation未尝试面试订阅3043Expected Third Arrival Given Five in Half an HourA Poisson process is observed on [0, 1 2 ] hours. Conditional on exactly 5 arrivals in that horizon, what is the expected time of the 3-th arrival?概率中等derivation未尝试面试订阅3046Exactly Two of Five Arrivals Before MiddayA Poisson process is observed on [0,1] hours. Conditional on exactly 5 arrivals in that horizon, what is the probability that exactly 2 arrivals occur before time 1 2 ?概率中等derivation未尝试面试订阅3047Exactly Three of Six Arrivals Before the First QuarterA Poisson process is observed on [0,2] hours. Conditional on exactly 6 arrivals in that horizon, what is the probability that exactly 3 arrivals occur before time 1?概率中等derivation未尝试面试订阅