Stirling, CLT, Poisson, Gamma

Here's another probability proof of Stirling's 1730 formula, which I stumbled upon yesterday. Let X_n be gamma(n,1). Then Z_n=(X_n-n)/\rootn tends to Z, the standard normal. Work a bit with the mean of Trunc(Z_n), and see that it is \rootn e^(-n) n^n/n!. Which has to tend to the mean of Trunc(Z), 1/\sqrt{2 \pi}. End of proof.

https://www.facebook.com/groups/1589206911336271/posts/3853571988233074/ 

So perhaps a subset of the December 2024 exam questions might have been mentioned or pointed to earlier in the FocuStat group.