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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3048Exactly One of Four Arrivals in the First Ten MinutesA Poisson process is observed on [0, 1 2 ] hours. Conditional on exactly 4 arrivals in that horizon, what is the probability that exactly 1 arrivals occur before time 1 6 ?概率中等derivation未尝试面试订阅3049Exactly Four of Seven Arrivals Before One Hour MarkA Poisson process is observed on [0, 3 2 ] hours. Conditional on exactly 7 arrivals in that horizon, what is the probability that exactly 4 arrivals occur before time 1?概率中等derivation未尝试面试订阅3051Earliest Arrival After 20 MinutesA Poisson process is observed on [0,1] hours. Conditional on exactly 4 arrivals in that horizon, what is the probability that the earliest arrival occurs after time 1 3 ?概率中等derivation未尝试面试订阅3052Latest Arrival Before 45 MinutesA Poisson process is observed on [0,1] hours. Conditional on exactly 5 arrivals in that horizon, what is the probability that the latest arrival occurs before time 3 4 ?概率中等derivation未尝试面试订阅3053Earliest Arrival After Half the WindowA Poisson process is observed on [0, 3 2 ] hours. Conditional on exactly 3 arrivals in that horizon, what is the probability that the earliest arrival occurs after time 3 4 ?概率中等derivation未尝试面试订阅3056One Arrival in Each ThirdA Poisson process is observed on [0,1]. Conditional on exactly 3 arrivals in the hour, compute the probability of the stated occupancy pattern across equal subintervals.概率困难derivation未尝试面试订阅3061Expected Number of Arrivals in the First 20 Minutes Given Nine TotalA Poisson process is observed on [0,1] hour. Conditional on exactly 9 arrivals in the hour, what is the expected number of arrivals in the first 20 minutes?概率简单derivation未尝试面试订阅3062Expected Number of Arrivals in the Middle Half Given Eight TotalA Poisson process is observed on [0,1] hour. Conditional on exactly 8 arrivals in the hour, what is the expected number of arrivals in the middle 30 minutes?概率简单derivation未尝试面试订阅