Imagine \(X\) has this cdf:

\[ F(x)=\frac{1}{1+\exp\left(-\frac{x-\mu}{s}\right)},\quad x\in\mathbb{R}. \]

\(\mu\in\mathbb{R}\) and \(s>0\) are just constants.

  1. What is the pdf of \(X\)?
  2. What is the mean of \(X\)?