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