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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5999Forward Wait from a Spontaneous GlanceBuses arrive at a stop as a Poisson process with rate 10 per hour. You walk up at an arbitrary moment, unsynchronized with the buses. What is the expected time, in minutes, until the next bus arrives?概率困难数值题未尝试免费6000Window for a 90% Chance of an ArrivalQuote updates arrive as a Poisson process with rate 5 per hour. How long a window, in minutes, must you watch so that the probability of seeing at least one update is exactly 0.9? Give a decimal to one place.概率中等数值题未尝试免费6001Equally Likely Adjacent CountsArrivals follow a Poisson process. Over a fixed observation window the count N satisfies P(N=2)=P(N=3). Given this, compute P(N=3) as a decimal to three places.概率困难数值题未尝试免费6002Exactly Four in an Eighteen-Minute WindowCancellations hit an order book as a Poisson process with rate 10 per hour. What is the probability that exactly 4 cancellations occur in an 18-minute window? Give a decimal to three places.概率简单数值题未尝试免费6003Ratio of Adjacent Count ProbabilitiesTrades print as a Poisson process with rate 12 per hour. Over a 20-minute window with count N, what is the ratio P(N=5)/P(N=4)? Give a decimal.概率简单数值题未尝试免费6004Short-Window Linear Approximation ErrorSpikes arrive at a detector as a Poisson process with rate 3 per minute. For a very short 0.5-second window the probability of at least one spike is often approximated by t. What is the absolute error of that approximation, i.e. t - P(N\ge 1)? Give a decimal to four places.概率中等数值题未尝试免费6005Empty Interval Between Two Clock TimesAlarms trip as a Poisson process with rate 6 per hour. What is the probability of zero alarms during the interval from minute 10 to minute 25 (a 15-minute span starting partway through)? Give a decimal to three places.概率中等数值题未尝试免费6006Waiting Time Exceeds Three Quarters of an HourService requests arrive as a Poisson process with rate 4 per hour. What is the probability that the waiting time to the first request exceeds 45 minutes? Give a decimal to three places.概率简单数值题未尝试免费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