Following the highly-cited paper, "Estimation of Entropy and Mutual Information" (Liam Paninski, link at the end), it is mentioned that the expectation of Pearson's chi-square functional (divergence) equals to,
\begin{equation*} E_{p}\left[ \chi ^{2}( p_{N,i} ;p)\right] =\frac{|supp( p) |-1}{N} \end{equation*}
Where |supp(p)| denotes the support of p (i.e. non-zero discrete probabilities), N denotes the number of samples used to estimate the true (discrete) probability, denoted by p.
However, I cant seem to derive this by myself nor I can find this derivation elsewhere. Is it a mistake?
Edit: attached link: https://www.stat.berkeley.edu/~binyu/summer08/L2P2.pdf
