NOTE 19U: To see the relation between var(d_ij) and var(x_i), consider the deviation from the mean:

The expectation of the square of this deviation is found by summing the expectations of the squares of each term, because the x_i are independent of each other (i.e., E[x_ix_j] = 0, E[x_i²] = var(x_i)). So,