I do this:
$$x_1, x_2, ..., x_{50} \sim N(0, 1)$$
and then mention of independence in the prose - no need for notation to communicate that part.
I do this:
$$x_1, x_2, ..., x_{50} \sim N(0, 1)$$
and then mention of independence in the prose - no need for notation to communicate that part.