Does anyone agree or disagree with what I did above?
Suppose 50% of a population is distributed with a mean age of 35 and a s.d. of 12 and the other 50% is distributed with a mean age of 45 and a s.d. of 12. Let X be the age of a randomly selected individual from this population. I believe the mean and variance are calculated in the following manner:
E[X] = .5*35+.5*45 = 40
Var(X) = E[Var(X|Y)] + Var(E[X|Y]) = E[Var(X|Y)] + E[(E[X|Y])^2] - (E[X])^2 = .5*144 + .5*144 + .5*35^2 + .5*45^2 - 40^2 = 169.
Could someone just look this over? Thanks!