Say we select a permutation $\sigma: [n] \to [n]$ from the permutation of all numbers $\{1,...,n\}$.
$Q1$ Model the corresponding probability space.
Next, define $X$ as an RV for the number of fixed points of $\sigma$.
$Q2$ Determine $\mathbb E[X]$.
My ideas:
$Q1$ Define $\Omega:=\{\sigma: [n] \to [n]:\sigma\in\mathcal{S}_{n}\}$ and $\mathcal{F}=2^{\Omega}$ as a result of discreteness, furthermore:
$P(\{\sigma\})=\frac{1}{n!}$
$Q2$ $E[X]=\sum_{i=0}^{n}\frac{1}{n!}\times (n-i)$
I am not sure on $Q2$ though