Show that, with a non-uniform quantizer, the mean-square value of the quantization error is approximately equal to

Question:

Show that, with a non-uniform quantizer, the mean-square value of the quantization error is approximately equal to (1/12) Σi ∆2i pi, where ∆i is the ith step size and pi is the probability that the input signal amplitude lies within the ith interval. Assume that the step size ∆i is small compared with the excursion of the input signal.