Given that $X_i$ are $i.i.d. \ \forall i \ni \ 1\leq i \leq n $
Is it true that
if $T = \sum_iX_i$ then
$$f(x_1, x_2,....,x_n, T) = f(x_1, x_2,....,x_n) $$
if $f$ is normal, exponential or poisson?
Please see the following picture. I am confused about the jump in the last step.
