Let's say that X1, X2, ..., Xn are iids with mean u and variance sigma^2.

if I let t1 = (X1-u)/[root(n)*sigma],

if I let t2 = (X2-u)/[root(n)*sigma], etc

does that mean that t1, t2... etc are all independent identically distributed - iid's too??

my gut says yes, because t1 is just X1 (etc) adjusted by constants, right??