def compute_moments_weights_pairs_std(neighbors, weights):
    """
    Computes the expectations of the local pair-wise test statistic

    This version assumes variables are standardized,
    and so the moments are actually the same for all
    pairs of variables
    """

    N = neighbors.shape[0]
    K = neighbors.shape[1]

    # Calculate E[G]
    EG = 0

    # Calculate E[G^2]
    EG2 = 0

    #  Get the x^2*y^2 terms
    for i in range(N):
        for k in range(K):
            wij = weights[i, k]

            EG2 += (wij**2)/2

    return EG, EG2