On 3/9/2020 2:53 PM, Russell Standish wrote:
On Sun, Mar 08, 2020 at 10:10:23PM +1100, Bruce Kellett wrote:> > In order to infer a probability of p = 0.5, your branch data must have > > approximately equal numbers of zeros and ones. The number of branches > with > > equal numbers of zeros and ones is given by the binomial coefficient. For > large > > even N = 2M trials, this coefficient is N!/M!*M!. Using the Stirling > > approximation to the factorial for large N, this goes as 2^N/sqrt (N) > (within > > factors of order one). Since there are 2^N sequences, the proportion with > n_0 = > > n_1 vanishes as 1/sqrt(N) for N large. This is the nub of the proof you wanted.No - it is simply irrelevant. The statement I made was about the proportion of strings whose bit ratio lies within certain percentage of the expected value. After all when making a measurement, you are are interested in the value and its error bounds, eg 10mm +/- 0.1%, or 10mm +/- 0.01mm. We can never know its exact value.
It may seem counter intuitive, but as the sample length goes up the probability of each possible proportion goes down, including that of the true value. It goes down because there are more possible exact values.
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