Why nothing is mentioned about the standard deviation of a Bernoulli trial ?
Does it even make sense if I try to visualize it ?
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$\begingroup$Why nothing is mentioned about the standard deviation of a Bernoulli trial ?
Where? Standard textbooks will have some mention regarding the variance, at a minimum. Regardless, you (I) can derive it yourself (myself).
If $X$ is a Bernoulli trial with chance $p$, then $$E[X] =\sum_{k = 0}^1 kP(X = k) = 0\cdot(1-p)+1\cdot p = p,$$ and $$E[X^2] = \sum_{k = 0}^1 k^2P(X= k) = 0^2\cdot(1-p)+1^2\cdot p = p.$$
Hence $$\text{Var}(X) = E[X^2]-\{E[X]\}^2 = p-p^2 = p(1-p)$$ and so $$\text{SD}(X) = \sqrt{p(1-p)}.$$
$\endgroup$ $\begingroup$If $p$ is the probability of success, then the variance of a Bernoulli random variable is $p(1-p)$, hence the standard deviation is $\sqrt{p(1-p)}$.
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