Suppose that you have an iid sample: (Wn, Fn)=1 where Wn is person n's hourly wage and Fn is a binary variable equal to 1 if person n is female and 0 other- wise. Consider the linear model E[log( Wn) | Fn] = Bo + BIFn.(e) What is the asymptotic distribution of [3"? Which theorem guarantees this? (2 points) (f) Carefully describe a twosided, size as test of the null hypothesis from part (a) using your data. Again, you can be concise, but you must provide enough details that someone else could replicate your approach. Do not just say What command you would use in the R. programming language. (4 points) Basic Stats/Probability Some definitions for everything below: . X, Y, and Z are random variables . a, b, c, d are constants . Whenever you see ux or ox, know that this is the mean and variance (respectively) of the random variable X . XN is a sample mean from a sample of random variables Xn drawn from the same distribution. s' is the sample variance calculated from a sample of X. Most of the rules follow almost immediately from the basic definitions, so you should test yourself by trying to prove each of them. It will also help you a lot if you know these rules like the back of your hand. . Efax + by] = aE[X] + bE[Y] . C( X, Y ) = E[(X - UX) ( Y - MY )] = C(Y, X) . C(a + bX, Y) = aC(X, Y) = C(a + bX, c+ dY) = adC(X, Y). . C(aX + by, Z) = aC(X, Z) + bC(Y, Z) . X LY = C(X, Y) = 0 . V[ X + Y] = X +Y+2C(X, Y) . = VIEn Xn] = En [X] if X1 l X2... I XN . E[XN] = UX . V[XN] = MV[X] if X1 1 X2... I XN (i.e. iid sample) . EE[XY] = E[X] (Law of Iterated Expectations) . E[XY] = 0 = E[XY] = 0 . E[X|Y] = a = C(X, Y) = 0 . If X ~ N( ux, ox), Y ~ N(uy, of) and Z = X + Y, then Z ~ N(ux + My, 03 + oz + 20xx) where oxy = C(X , Y). . When Xx comes from an iid sample and V[X']