We could use the confidence interval to find a minimum probability. Let's say that the error is given as . So:
is the lower bound of in the confidence level. Let's call Q(X) the probable expectation that the next entry in the sequence is X. So, . We can take the derivative with respect to to find the value of which maximizes :
Now, recall our relationship:
And substitute for E:
It seems like we should be able to do better than this, though.