Incorrect variance of normal inverse gamma posterior predictive (in documentation at least)

[jmh530]

I am looking at your documentation for the variance of the posterior predictive of the normal inverse gamma available here:
https://gnpalencia.org/cprior/formulas_models_normal.html

This relies on Kevin Murphy's 2007 paper. However, it looks like he specifies the t distribution in terms of the variance, rather than standard deviation. So you derive the wrong variance as a result. It should be something like beta * (1 + 1 / lambda) / (alpha - 1).