I am quite new in the probabilistics field, and I am trying to figure out how would drawing n samples from a probability distribution perform.
Suppose We have a non-uniform probability distribution D from which we drew n successive samples, and say that M is the mean of these n samples. Is it true that the standard deviation of these n samples would be $\sigma_M = \frac{\sigma}{\sqrt{n}}$ , where $\sigma$ is the standard deviation of the probability distribution D? Would that relation be true for any number of drawn samples n (1, 2, 3, ....)? And if for example we draw another sample to have n+1 samples, would the relation still be correct with the added sample?
Also, is there any other relation or equation that tells us how would drawing n samples act?