# How do I obtain the weight and variance of a k-means cluster?

I am trying to reproduce the results of this paper, but using python and the HMMlearn library instead of matlab. The paper describes a procedure for using HMM (Hidden Markov Model) in order to predict stock prices.

The paper details the use of a 4-state, 5-mixture Gaussian distribution as the model. The transition probabilities and the initial state probabilities are uniform, however the emission probabilities are determined based on the results of a k-means algorithm using the data-set of existing stock prices.

This latter part is where I have gotten stuck, the paper advises to use the means, variance and weight of each cluster returned from the k-means algorithm as the mean, variance and weight of each component of the mixture. As I understand it the mean of the cluster is simply the center of each centroid, however I'm not sure how you would obtain the variance or the weight.

TL;DR Given a 3 dimensional dataset X (in the form [[a, b, c], [d, e, f]...]) and using the k-means algorithm where k = 5 (k = number of mixture components), how would I determine the weight and variance of each cluster?