MLE for normal distributions

In the previous section, we had a model with a single parameter. In this section, we will apply the same concepts to a slightly more complex model. We will try to learn the parameters of a normal distribution (also known as the Gaussian distribution) from a given observed data. As we know, the normal distribution is parametrized by its mean and standard deviation and the distribution is given as follows:

Here, µ is the mean and σ is the standard deviation of the normal distribution.

As we discussed earlier, for estimating parameters using MLE we would need some observed data, which, in this case, we are assuming ...

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