In my understanding, I let make a example.
For example, you can see in the following picture.
Consequently, We want to find ^sigma. and We have already known the observation data(which is random data such as C) and bin(0.3).
To know "the estimated standard deviation ^sigma", First of all,
- Find Likelihood for each bins with observed data( for example, data of C).
- Find Maximum Likelihood among previous Likelihood values(from 1).
- the Maximum Likelihood is "the estimated standard deviation ^sigma". Am I wrong? In other words, the Maximum Likelihood (^sigma) represent all bins's Likelihood values.