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3541Start Needed for a 70% Upper-Hit Probability on [0, 6]For Brownian motion on [0, 6], at what starting point x is the probability of hitting 6 before 0 equal to 0.7?随机过程中等derivation未尝试面试订阅3542Upper-Hit Probability From x = 1 on [-3, 5]For Brownian motion started at x = 1 inside [-3, 5], what is the probability of hitting 5 before -3?随机过程中等derivation未尝试面试订阅3543Symmetric Interval Size for a 2/3 Upper-Hit ProbabilityBrownian motion starts at x = 1 inside [-L, L]. What L makes the probability of hitting +L before -L equal to 2/3?随机过程中等derivation未尝试面试订阅3544Lower Barrier Needed for a 40% Upper-Hit ProbabilityBrownian motion starts at x = 1 and has upper barrier 4 and lower barrier a < 1. What a makes the probability of hitting 4 before a equal to 0.4?随机过程中等derivation未尝试面试订阅3545Upper Barrier Needed for a 1/3 Hit Probability From x = 2Brownian motion starts at x = 2 with lower barrier 0 and upper barrier b > 2. What b makes the probability of hitting b before 0 equal to 1/3?随机过程中等derivation未尝试面试订阅3546Expected Exit Time From [0, 5] Started at 2For Brownian motion started at x = 2 inside [0, 5], what is the expected exit time from the interval?随机过程困难derivation未尝试面试订阅3547Expected Exit Time From [-2, 4] Started at 1For Brownian motion started at x = 1 inside [-2, 4], what is the expected exit time from the interval?随机过程困难derivation未尝试面试订阅3548Symmetric Half-Width Needed for Expected Exit Time 8Brownian motion starts at x = 1 inside [-L, L]. What L makes the expected exit time equal to 8?随机过程困难derivation未尝试面试订阅3549Lower Barrier Needed for Expected Exit Time 12Brownian motion starts at x = 2 with upper barrier 5 and lower barrier a. What a makes the expected exit time equal to 12?随机过程困难derivation未尝试面试订阅3550Upper Barrier Needed for Expected Exit Time 6 From x = 1.5Brownian motion starts at x = 1.5 with lower barrier 0 and upper barrier b. What b makes the expected exit time equal to 6?随机过程困难derivation未尝试面试订阅3551Average Upper-Hit Probability With Uniform Start on [0, 6]If the starting point X is uniform on [0, 6], what is the average probability of hitting 6 before 0?随机过程困难derivation未尝试面试订阅3552Average Exit Time With Uniform Start on [0, 6]If the starting point X is uniform on [0, 6], what is the expected exit time from [0, 6]?随机过程困难derivation未尝试面试订阅3554Average Exit Time With Uniform Start on [-3, 3]If X is uniform on [-3, 3], what is the expected exit time from [-3, 3]?随机过程困难derivation未尝试面试订阅3555Conditional Upper-Hit Probability From the Upper Half of [0, 8]If X is uniform on [0, 8] conditioned on X > 4, what is the average probability of hitting 8 before 0?随机过程困难derivation未尝试面试订阅3556Interval Width When the Start Is One-Third of the Way UpBrownian motion starts at x = b/3 inside [0, b]. What b makes the expected exit time equal to 8?随机过程中等derivation未尝试面试订阅3557Expected Exit Time When Upper-Hit Probability Is 2/3 on [0, 9]Brownian motion starts somewhere in [0, 9] such that the probability of hitting 9 before 0 is 2/3. What is the expected exit time?随机过程中等derivation未尝试面试订阅3558Symmetric Interval and Start Matching Two TargetsBrownian motion starts at x inside [-L, L]. If the probability of hitting +L before -L is 0.75 and the expected exit time is 12, what is x?随机过程中等derivation未尝试面试订阅3559Lower Barrier and Hit Probability From a Target Exit TimeBrownian motion starts at x = 1 with upper barrier 5. The lower barrier a is chosen so that the expected exit time is 8. What is the resulting probability of hitting 5 before a?随机过程中等derivation未尝试面试订阅3560Start Needed to Match Both a Probability and an Exit Time on [0, 10]Brownian motion starts at x inside [0, 10]. If the probability of hitting 10 before 0 is 0.6, what is the expected exit time?随机过程中等derivation未尝试面试订阅3561Why the Hitting Probability Is HarmonicWhy does the probability of hitting the upper barrier before the lower barrier end up being a linear function of the start x for Brownian motion?随机过程中等essay未尝试面试订阅