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Why is E{[X-E(X)][(X-a)-E(X-a)]} = Var(X)?
For the second last line, how does the numerator equal to Var(X)?
I know that Var(X) = E{[X-E(X)]²}
I can't quite figure out what's going on though. How does the constant a disappear?
1 Answer
- Anonymous2 years agoFavorite Answer
If a is a constant then:
1) E(a)= a and
2) E(X – a) = E(X) – E(a)
which gives E(X – a) = E(X) – a.
This means one part of your expression is
(X – a) – E(X –a)
= X - a – (E(X) – E(a))
= X - a – (E(X) – a)
= X – E(X)
So the constant (a) has cancelled out.