A secretery introduces $9$ adressed letters into $9$ envelops. $X$ represents the number of letters in the correct envelope.
What's $\operatorname{var}(X)$ and expected value? I'm assuming it should be a Poisson distribution?..I'm new to this chapter and I'm still trying to understand how this problems go
It is not a Poisson distribution, possion variable can take arbitarily large positive number but the maximum value of $X$ is $9$.
Hint:
Let $X=\sum_{i=1}^9 X_i$ where $X_i$ takes value $1$ if the $i$-th envelop has the right letter and $0$ otherwise.
Then we have $$X^2=\sum_{i=1}^9 X_i^2+\sum_{i \neq j} X_iX_j$$
and use linearity of expectation.