Supose X has density f (x) and Y X. You have a random sample {Y1, ...,Yn}

Supose X has density f (x) and Y Æ ¹Å¾X. You have a random sample {Y1, ...,Yn} from the distribution of Y .

(a) Find an expression for the density fY (y) of Y .

(b) Suppose f (x) Æ C exp(¡a(x)) for some known differentiable function a(x) and some C. Find C.

(Since a(x) is not specified you cannot find an explicit answer but can express C in terms of an integral.)

(c) Given the density from part

(b) find the log-likelihood function for the sample {Y1, ...,Yn} as a function of the parameters (¹,¾).

(d) Find the pair of F.O.C. for theMLE (b¹,b¾

2). (You do not need to solve for the estimators.)