Editing Gauss–Markov theorem (section)

==Scalar case statement==
Suppose we are given two random variable vectors, <math> X \text{, } Y \in \mathbb{R}^k </math> and that we want to find the best linear estimator of <math>Y</math> given <math>X</math>, using the best linear estimator
<math> \hat Y = \alpha X  + \mu </math> 
Where the parameters <math> \alpha  </math> and <math> \mu </math> are both real numbers.

Such an estimator <math> \hat Y </math> would have the same mean and standard deviation as <math> Y</math>, that is, <math> \mu _{\hat Y}  = \mu _{Y} , \sigma _{\hat Y} = \sigma _{Y}</math>.

Therefore, if the vector <math> X </math> has respective mean and standard deviation <math> \mu _x , \sigma _x </math>, the best linear estimator would be

<math> \hat Y = \sigma _y \frac{(X  - \mu _x )}{ \sigma _x } + \mu _y </math> 

since <math> \hat Y </math> has the same mean and standard deviation as <math>Y</math>.