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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3063At Least One Arrival in the Final Quarter Given Four TotalA Poisson process is observed on [0,1] hour. Conditional on exactly 4 arrivals in the hour, what is the probability that at least one arrival falls in the final quarter-hour?概率中等derivation未尝试面试订阅3064Expected Idle Time Before the First Arrival Given Three TotalA Poisson process is observed on [0,1] hour. Conditional on exactly 3 arrivals in the hour, what is the expected idle time from 0 until the first arrival?概率中等derivation未尝试面试订阅3065Expected Idle Time After the Last Arrival Given Five Total in Two HoursA Poisson process is observed on [0,2] hours. Conditional on exactly 5 arrivals in the two-hour horizon, what is the expected idle time from the last arrival until hour 2?概率中等derivation未尝试面试订阅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