Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
Z_1/√n, Z_2/√n, …, Z_n/√n are also identical random variables. So we award ourselves the liberty to assume the following: Z_1/√n = Z_2/√n = … = Z_n/√n = Z/√n. Therefore using property (7b) we get: MGF of n i.i.d. random variables (Image by Author) Finally, we’ll also use the property (6) to express