As we may know, Bayes' theorem can be formulated as: P(jx)=(P(xj)P(j))/(P(x)) where x and j denote events, and P(xj) can be depicted by the Gaussian function. When there are two clusters set to group (i.e., when j=2 ), show how to compute probability P(x). As Bayes' theorem is applied to Gaussian mixture modelling (GMM) in 1-D case, the conditional probability becomes P(xj)=(1)/(sqrt(2pi sigma))e^(-((x-mu)^(2))/(2sigma^(2))) where mu and sigma respectively denote the mean and the standard deviation of the 1-D input samples x. After the clustering number is confirmed, what parameters are to be estimated and updated? What are the difference and the similarity between GMM and K-means for clustering