I would like to know and understand the answer of this small maths problem on probabilities. I looked around but I don't find the answer and it really bugs me since I need it for my data analysis!
I have a fake dice of n faces and I don't know the face probabilities. To know the probabilities, I do a measurement: I roll the dice N times and I compute de probability of each faces with: $$ P = \frac{n_i}{N} $$
If N is very large, the measurement should be very precise, if N is small the measurement is not precise at all.
Now I would like to know the standard deviation of the probability measurement for each faces, in other terms what is the error of the measurement as a function of N (I guess) ?
Thanks a lot !
You can calculate the sample variance for every face (given that they have different probability) as $$ \sigma^2 = Np(1-p) $$ Where N is the number of trials and p the portion of true events between the number of trials. Edit for completeness: you need to calculate a binomial random variable for every face.