Let Yi,...,Y„ be independently distributed normal random variables with

where p 1? p2, P3> and ct2 are unknown parameters a n d xh z h i = 1,...,/?
are known constants.

(a) Find the maximum-likelihood estimators pi, p2, p3, d 2 of p l9 p2, p3, a 2, respectively.

(b) Find the distribution of p,, / = 1,2,3.

(c) Find the distribution of

(d) Do parts (a),

(b) and

(c) with z, = x 2.

E(Y) BBx; + B3Zi var(Y) =