I have the following question which I will first describe by my current understanding of binomial distribution / Bernoulli random variable.
(1) The coin has two sides, 0 or 1. The outcome of flipping the coin follows a binomial distribution law and so the coin is a Bernoulli random variable.
And so it is within a set of independent coins. Flipping 3 independent coins 3 times, leading results such as [[0,1,1],[1,1,1],[0,1,0]] allows to compute three distinct error bars on the "true" value of each coin variable (which should be 0.5, and even though in this example we would need more coinflips).
So now, my problem.
(2) I have one sample which can be 0 or 1. There is no way to "flip" the sample here, it is 0 or 1 and this 0 or 1 is the true value of the sample.
I do 3 predictions on this sample, yielding [0,1,1]. And so I can do with a set of independent samples each following the same rule, so yielding [[0,1,1],[0,0,1],[0,1,0]].
And my question:
Are (1) and (2) the same thing? More precisely, is the sample a random Bernoulli variable as the coin is? And if so, can I compute the same error based on sqrt(P(1-P)/N) with P = predtrue/predfalse.
If I am out of the Bernoulli frame for (2), how to calculate an error for those prediction?
Any help would be much appreciated!