<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def weighted_minkowski(x, y, w=_mock_identity, p=2):
 """A weighted version of Minkowski distance. ..math:: D(x, y) = \left(\sum_i w_i |x_i - y_i|^p\right)^{\frac{1}{p}} If weights w_i are inverse standard deviations of data in each dimension then this represented a standardised Minkowski distance (and is equivalent to standardised Euclidean distance for p=1). """

    result = 0.0
    for i in range(x.shape[0]):
        result += (w[i] * np.abs(x[i] - y[i])) ** p

    return result ** (1.0 / p)