Estimating the parameters of the Gaussian from data

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Now, before we go on, let's just not derive but simply state and its into it enough to state it.
How do we estimate the mean on the variance of the calcium? Let's go back to some.
This one here.
So imagine we've got some data points.
We've got those data points and they all belong to the same class.
There are green things or blue things or or they're all words on Nurse.
How do we estimate Mu and Sigma? Well, there's these parameters here, Mu and Sigma.
We're just going to state without proof, because so obvious.
I think you're just going to accept it in the best possible estimate from you.
They're just the average value of the data points.
The best estimate of the mean of the calcium is the mean of the data about the empirical means.
Unsurprisingly, the best estimate of the standard deviation is the standard deviation of the data about that data point we could derive from first principles.
We're not going to beyond our scope and in fact, those estimates those estimates of taking the average of the data and taking the standard deviation of the data.
These empirical estimates of meaning VarianMS very important there, Well motivated.
And they're the ones that make the training data as likely as possible toe have been generated from this particular problem to distribution, So the estimates are what we call maximum likelihood estimates.
There are other ways of estimating the prime minister probably distributions, but this is the simplest and the most obvious, and the one we're going to use the maximum likelihood estimates.