Say you have normally distributed iid random variables, $X_1, X_2,....,X_n$ with with known mean and variance. And you wanted to find the limiting distribution of one of these
$Y_n = max\{X_1, X_2,....,X_n\}$ or $T_n = min\{X_1, X_2,....,X_n\}$
Is it possible to find the limiting distribution with using the mgf of the normally distributed random variables? If so, how does one go about it or is this a bad tactic?
I can find only a general example or two using the uniform distribution.
