By Fearn T., Brown P.J., Besbeas P.
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However, he did not calculate a probability for the error to exceed a specific quantity but looked for a best choice to represent the data. His argument can be summarized in the following form. A certain event E has occurred which has different probabilities under different, mutually exclusive conditions Cj • Then one should assume that condition being operative which supplies the observed event with the highest conditional probability P(EiCJ This is clearly a precursor to R. A. Fisher's maximum likelihood principle.
Gauss took the mean as given, and found the normal distribution as one base to derive the mean as most likely value. He also gave intuitively acceptable mathematical restrictions from which he could derive the distribution of errors to be normal. Gauss explored the relationship between four concepts; the mean as the best value to take from a series of measurements; the nonnal distribution for describing variation of errors; the maximum likelihood method to take the best value from a series of measurements; and the method of least squares to derive the best value replacing a series of measurements.
Division of stakes. The problem deals with the fair division of stakes if a series of games has to be stopped before completion. At the beginning of a series of games two players A and B bet equal stakes. The player to win a certain number of single games first wins the whole stake. However, the series has to be interrupted before one of the players has reached the required number of points and the stakes have to be divided. If five games are required to win, and the score is 4:3 in favour of A, what is the fair division of stakes?