The Kappa statistic was defined as following: $\kappa = \displaystyle\frac{p_o-p_e}{1-p_e}$, where $ p_o = \displaystyle\sum_{i=1}^{k} p_{ii}$ is the observed agreement, and $p_c = \displaystyle\sum_{i=1}^{k} p_{i.} p_{.i}$ is the chance agreement.
I saw the following conclusion from a reference book: $Var(\kappa)=\frac{1}{N(1-p_e)^2}[p_e+p_e^2-\sum_{i=1}^{k} p_{i.}p_{.i}(p_{i.}+p_{.i})]$ and the mean $E(\kappa)$ of $\kappa$ is 0.
How to compute the variance of $\kappa$