Take the tour ×  If $X_1, X_2,...$ is a sequence of pairwise
independent, identically distributed random variables then
$|X_1| I_{|X_1|>b}$, $|X_2|.I_{|X_2|>b}$,... is also pairwise
independent, identically distributed? ($I_{|X_i|>b}$ means
$I_{|X_i|>b} = 1$ if $|X_i|>b$ and $I_{|X_i|>b} = 0$ otherwise).
Thanks.  share|improve this question add comment  1 Answer  If
you are talking about the pairwise independence, you always only
compare pairs hence it is sufficient to consider a single pair.
You have $X_1 1_{(X_1>b)} = f_b(x_1)$ where $$ f_b(x) = x\cdot
1_{(x>b)}. $$ Since measurable functions of independent randon
variables are independent random variables, you have the
pairwise independence. Identical distribution comes from the
fact that whenever $X_i\sim \mu_i$ then $f(X_i)\sim \mu_i\circ
f^{-1}$ which is an image probability measures. Since $\mu_i =
\mu_j$ you have that image measures (distribution of $f_b(X_i)$
and of $f_b(X_j)$) are equal as well.  So, the answer is: yes.
The answer will still hold to