Let \(\kappa_{0}=ho \zeta(y) /(1-ho+ho \zeta(y))\) be the exceedance probability, and let \(\kappa_{r}\) be the \(r\) th derivative of \(\log (1-ho+ho \zeta(y))\). For \(\zeta(y) \simeq e^{y^{2} / 2} / y^{2}\) for large \(y\), show that Eddington's formulae give

\[
E(X \mid Y) \simeq \kappa_{0}\left(y^{2}-2ight) /|y|, \quad \operatorname{var}(X \mid Y) \simeq \kappa_{0}\left(1-\kappa_{0}ight)\left(y^{2}-3ight)+\kappa_{0}^{2}
\]

for large \(y\). Discuss the implications for mean shrinkage and variance inflation.