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251Remaining Time to HTH After Seeing HTA fair coin has been flipped for a while, and the current suffix of the observed sequence is exactly HT (that is, the last two flips are HT). From this point onward, what is the expected additional number of flips until HTH appears for the first time?概率简单数值题未尝试免费252Remaining Time to HTH After Seeing HA fair coin is being flipped repeatedly. You are told that the current observed suffix is exactly H. Starting from that suffix-state, what is the expected additional number of flips until HTH first appears?概率简单数值题未尝试免费253Expected Time Until Either HHT or HTH AppearsA fair coin is flipped repeatedly. Let T be the first time that either HHT or HTH appears as a consecutive length-3 block. Find E[T].概率简单数值题未尝试免费254Expected Time Until Either HTH or TTH AppearsA fair coin is flipped repeatedly. Let T be the waiting time until either HTH or TTH appears. Find E[T].概率简单数值题未尝试免费255Three Heads in a RowA fair coin is flipped repeatedly. What is the expected number of flips until the pattern HHH first appears?概率中等derivation未尝试免费256Waiting for THTTA fair coin is flipped repeatedly. Find the expected number of flips until THTT first appears.概率中等derivation未尝试免费257Overlap Penalty for HTHTA fair coin is flipped repeatedly. Let T be the waiting time until HTHT first appears. Compute E[T].概率困难derivation未尝试免费258Biased Coin Waiting Time for HHTA coin lands Heads with probability rac 3 5 and Tails with probability rac 2 5 , independently from flip to flip. What is the expected number of flips until HHT first appears?概率中等数值题未尝试免费259Resume from HT Toward HTH with a Biased CoinA coin lands Heads with probability rac 3 5 and Tails with probability rac 2 5 , independently on each flip. The current observed suffix is HT. From here, what is the expected additional number of flips until HTH first appears?概率中等数值题未尝试免费260ABA in a Uniform Three-Symbol StreamEach second, a monitoring system emits one symbol from \ A,B,C\ , independently and uniformly. What is the expected number of symbols until the pattern ABA first appears?概率中等derivation未尝试免费261Finish ABA After Already Seeing ABAn iid stream over \ A,B,C\ is uniform. You currently know that the observed suffix is exactly AB. What is the expected additional number of symbols until ABA first appears?概率简单数值题未尝试免费262Waiting for ABAB in a Uniform ABC StreamEach symbol in an iid stream is chosen uniformly from \ A,B,C\ . Find the expected waiting time until ABAB first appears.概率困难derivation未尝试免费263First Hit of ABA or BAAAn iid stream over \ A,B,C\ is uniform. Let T be the first time that either ABA or BAA appears. Compute E[T].概率中等derivation未尝试免费264Expected Time Until ABC or CBAA symbol stream is iid and uniform on \ A,B,C\ . What is the expected number of symbols until either ABC or CBA first appears?概率简单数值题未尝试免费265Nonuniform Stream Waiting for AABAAn iid source emits A,B,C with probabilities rac 1 2 , rac 1 3 , rac 1 6 respectively. Find the expected waiting time until AABA first appears.概率中等derivation未尝试免费266Nonuniform Stream Waiting for ABBAAn iid source emits A,B,C with probabilities rac 1 2 , rac 1 3 , rac 1 6 respectively. What is the expected number of emitted symbols until ABBA first appears?概率中等derivation未尝试免费267Nonuniform Stream Waiting for ABACAn iid source emits A,B,C with probabilities rac 1 2 , rac 1 3 , rac 1 6 respectively. Find the expected waiting time until ABAC first appears.概率困难derivation未尝试免费268ABCA in a Four-Symbol StreamEach symbol of an iid stream is chosen uniformly from \ A,B,C,D\ . Compute the expected waiting time until ABCA first appears.概率困难derivation未尝试免费269Finish ABCA After Current Suffix ABCAn iid stream over \ A,B,C,D\ is uniform. Suppose the current observed suffix is exactly ABC. From this point onward, what is the expected additional number of symbols until ABCA first appears?概率简单数值题未尝试免费270Rolls Until 1-2-3 AppearsA fair six-sided die is rolled repeatedly. What is the expected number of rolls until the consecutive pattern 1,2,3 first appears?概率中等derivation未尝试免费