# With EM algorithm, can you infer the location and variance of each “peak” in a pdf? Gaussian Mixture Models?

When I plot my data into bins, there is a frequency of data points per bin, which I can plot with a histogram. Based on this probability density function, I would like to find the maximum likelihood estimation of various parameters associated with this pdf.

How can I infer the number of "peaks" of this pdf? Is this possible using a Gaussian Mixture Model (let's say using Expectation Maximization)?

I believe in this case, we are inferring the location and variance of each "peak" using Gaussian clusters.

Secondly, how does one infer the number of clusters which model the data best?