Born2bwire
Diamond Member
- Oct 28, 2005
- 9,840
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The probability that he will reach the sleigh at 1:00 is 0, 1:10 0, etc., for each time you can compute the probability that he will reach the sleigh at that time (and not have been there earlier). The most likely time is the time that has the biggest probability. I don't think there's anything moot here.
That would be different than say the expectation value which is what I and others have tried to evaluate. For example, I could have a distribution where the probability is: y(1) = 0.7, y(2) = 0.2, y(3) = 0.1. In this case, under your definition, the most likely value is 1 since the probability is the highest here. However, the expected value is 1.4. Finding the time with the highest probability is a much more difficult problem as you each hour presents 64 possible states that you have to map into.