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Now for a simple example. Let's say you have a fair die. Each time you toss it, the probabily of each outcome is 1/6. So theory says we have a uniform distribution. Now toss the die 100 times and count how many times each value shows up. Now theory says on average each value shows up 1/6 of the time. However in any given sample (set of measurements), you can't expect this perfect a distribution every time. Why you ask? That is because each trial is independent of the prior ones. And in this situation I only tossed it 100 times and 100 is not a multiple of six, so not all bins can have the same number of counts. Since the counts must be integers and 100/6 = 16.6666666, you can see the one problem.
This can raise an unrealistic expectation. If we toss the die 102 times, can we then ask that each face of an honest die to turn up 17 times?
Jerry -- Engineering is the art of making what you want from things you can get. ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ
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