Recently I have been reading through the Lecture-One course material that can be found at this link.
Anyways, in section-2 the author shows the following step in his derivation of an optimal guess by minimizing the function MSE(a):
where Y is a random variable and a is the prediction we are to make.
My question is: What is the properties/steps the author takes from making this jump. Specially, how is this step true?
The rest of the derivation is straightforward but I am finding this step hard to see and through all the literature I am parsing through, I am not finding anything that exactly works.