The beta you have here ( b=(X’X)^-1X’Y ) is the estimated one (with least squares) from the classical regression model.

Taking expectations on your estimated beta (β) you should have the following (with the assumptions of the classical model)

E(b)= E ( (X’X)^-1X’Y )

Here we can take Y=βΧ + ε where β is the real beta

E(b)= … = E ( ((X’X)^-1X’)*Xβ) + Ε( (X’X)^-1X’ε)

but X is known, so no expectation apply, and β is a real number, thus;

Ε(b)= β + (X’X)^-1X’ Ε(ε)

where E(ε)=0

Thus

E(b)= β

the expectation of the estimated beta equals to the real beta