Quote:
Originally Posted by vbipin
Dear Professor,
Can you kindly explain how we can calculate this number. How can we ensure that the number is "sufficiently large"
Thanks,
Bipin

The probability for a single random point to be misclassified is, say,
. Therefore the variance for one point (1 if misclassified, 0 if classified correctly) is
which is at most 0.25 independently of
. If you average the misclassification value of 10000 points, the expected value will be
(which is what you want) and the variance will be at most 0.25/10000 (because of independence). The standard deviation which is the square root of this variance gives you an indication of the "error bar" around the expected value that you are likely to get in your estimate. In the multiplechoice setup, we want the error bar to be small enough to make it highly unlikely that your estimate will take you away from the correct answer to the nearest incorrect answer. This is why 10000 is "sufficiently large" in this case.