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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