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271Finish 1-2-3 After Already Rolling 1,2A fair six-sided die is rolled repeatedly. You already know that the current observed suffix is exactly 1,2. Starting from here, what is the expected additional number of rolls until 1,2,3 first appears?概率简单数值题未尝试免费272Three Consecutive Ones on a DieA fair six-sided die is rolled repeatedly. Let T be the waiting time until three consecutive 1s first appear. Compute E[T].概率困难derivation未尝试免费273Return-and-Overlap Pattern 1-2-1 on a DieA fair six-sided die is rolled repeatedly. Find the expected waiting time until the consecutive pattern 1,2,1 first appears.概率困难derivation未尝试免费274Either 123 or 321 on a Fair DieA fair six-sided die is rolled repeatedly. Let T be the first time that either 1,2,3 or 3,2,1 appears as a consecutive length-3 block. Compute E[T].概率困难derivation未尝试免费275Waiting for HHTHA fair coin is flipped repeatedly. What is the expected number of flips until HHTH first appears?概率中等derivation未尝试免费