Likelihood
To understand the probability distribution that the data follows, we’ll look at an explicit example of how a random component is incorporated into data.
A simple probabilistic model
We’ll start with the simplest way in which we can introduce a random component into our observations of the response (target) variable 
, namely by adding noise to a deterministic quantity. In fact, we’ll just consider the observations 
in our dataset to be noise-corrupted versions of a model output 
. So, we have this relationship:
Eq. 1
Here, 
is the noise value that has been added to the model output 
to get the observation 
for the 
datapoint. The value 
is a random variable. Without loss of generality, we can assume its expectation value is zero, so we have 
. We can make this assumption because if the expectation of was non-zero, it would mean we have a non-zero deterministic average contribution from that we could just absorb into the definition of 
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