第 8 / 41 页
非代码面试题
显示 20 / 814 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
163Expected Number of Exact Triple CollisionsFor n independent uniform birthdays on an m-day calendar, what is the expected number of unordered triples of people that share an exact birthday?概率中等derivation未尝试面试订阅164Exactly One Pair Among Four BirthdaysFour people have independent uniform birthdays on a 365-day calendar. What is the probability that there is exactly one matching pair and no larger collision?概率困难derivation未尝试面试订阅165Expected Number of People Who Share Someone's BirthdayFor n independent uniform birthdays on a 365-day calendar, what is the expected number of people whose birthday is shared by at least one other person?概率困难derivation未尝试面试订阅166Expected Cross-Team Birthday MatchesTeam A has 12 people and team B has 18 people. Birthdays are independent and uniform over 365 days. What is the expected number of cross-team exact birthday matches (one person from A and one from B)?概率简单数值题未尝试免费167Expected Days Hit by Both GroupsGroup A has a people and group B has b people, with independent uniform birthdays on a 365-day calendar. What is the expected number of calendar days on which both groups have at least one birthday?概率中等derivation未尝试面试订阅168Pair Expectation Under a Nonuniform CalendarBirthdays fall on days 1 through m with probabilities p1,...,pm, not necessarily uniformly. For n independent people, what is the expected number of unordered matching pairs?概率中等derivation未尝试面试订阅169Expected Pairs Within Two DaysOn a 365-day circular calendar, what is the expected number of unordered pairs among n independent uniform birthdays whose birthdays are at circular distance at most 2 days?概率困难derivation未尝试面试订阅170Collision Risk for the Next Arrival Given Distinct Existing BirthdaysSuppose n existing birthdays are all distinct on a 365-day calendar. A new person's birthday is then drawn uniformly and independently. What is the probability the new arrival creates an exact collision?概率困难derivation未尝试面试订阅171Expected Pair Count With One Holiday Twice as LikelyOn a 366-point calendar, one special holiday has probability 2/366 and each of the other 364 days has probability 1/366. For n=30 independent birthdays, what is the expected number of unordered matching pairs?概率简单数值题未尝试免费172Poisson Approximation Threshold for Near CollisionsUse the pair-Poisson approximation for birthdays on a 365-day circular calendar where a pair counts as a collision if the birthdays are the same day or one day apart. What is the smallest n for which the approximated collision probability exceeds 50%?概率简单数值题未尝试免费173Expected Number of Singleton BirthdaysFor n independent uniform birthdays on a 365-day calendar, what is the expected number of people whose birthday is unique in the sample?概率中等derivation未尝试面试订阅174Expected Number of Days With Exactly Two BirthdaysFor n independent uniform birthdays on a 365-day calendar, what is the expected number of calendar days that receive exactly two birthdays?概率中等derivation未尝试面试订阅175Expected Number of Days With at Least Three BirthdaysFor n independent uniform birthdays on a 365-day calendar, what is the expected number of calendar days that receive at least three birthdays?概率困难derivation未尝试面试订阅176Server A Empty but Server B ActiveSix labeled jobs are independently routed to four labeled servers A, B, C, D with equal probability. How many assignments leave server A empty but give server B at least one job?概率简单数值题未尝试免费177Odd Load on a Tagged ServerFive labeled packets are independently assigned to three labeled servers. In how many assignments does server A receive an odd number of packets?概率简单数值题未尝试免费180Hypergeometric Moments from an UrnAn urn contains 20 balls: 8 red and 12 blue. You draw 5 balls without replacement. Let X be the number of red balls drawn. Derive E[X] and Var (X) using indicator random variables. Express each answer as an exact fraction.概率困难derivation未尝试免费181Coupon Collector with Four TypesA cereal box contains one of 4 equally likely coupon types. You buy boxes one at a time. What is the expected number of boxes you must buy to collect all 4 types?概率简单数值题未尝试免费182Expected Occupied Servers After a Tagged AssignmentA tagged job is known to have been routed to server A. Then five additional labeled jobs are independently routed uniformly to the four servers A, B, C, D. What is the expected total number of occupied servers?概率中等数值题未尝试免费183Collision Probability in the Occupancy ModelFive distinguishable balls are thrown independently and uniformly at random into 12 distinguishable urns. What is the probability that at least two balls land in the same urn? Give an exact fraction.概率中等数值题未尝试免费185Coupon Collector: Mean and VarianceA machine dispenses one of n = 4 equally likely prize types per trial. Let T be the number of trials needed to collect all 4 types. Derive both E[T] and Var (T) by decomposing T into independent geometric phases. Express each answer as an exact fraction.概率困难derivation未尝试免费