Suppose that Xi N(X ,2 X ) : i 1, . . . ,n1 and

Suppose that Xi » N(¹X ,¾2 X ) : i Æ 1, . . . ,n1 and Yi » N(¹Y ,¾2 Y ), i Æ 1, . . . ,n2 are mutually independent. Set Xn1

Æ n¡1 1

Pn1 iÆ1 Xi and Y n2

Æ n¡1 2

Pn2 iÆ1 Yi .

(a) Find E h

Xn1

¡Y n2 i

.

(b) Find var h

Xn1

¡Y n2 i

.

(c) Find the distribution of Xn1

¡Y n2 .

(d) Propose an estimator of var h

Xn1

¡Y n2 i

.