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Fig. 11.
The convolution of  with  . |
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above and from what follows that fewer trials can be allocated to attain the same reduction of q(N - n, n).The expected loss is reduced accordingly.) |
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The observation that q' and hence q(N - n, n) decreases exponentially with n makes it clear that, to minimize loss as N increases, the number of trials allocated the observed best, N- n, should be increased dramatically relative to n. This observation (which will be verified in detail shortly) enables us to simplify the expression for x0. Whatever the value of s2, there will be an N0such that, for any  , for n close to its optimal value. (In most cases of interest this occurs even for small numbers of trials since, usually, s1 is at worst an order of magnitude or two larger than s2.) Using this we see that, for n close to its optimal value, |
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