Let Z1, Z2, . . . , Z10 iid Normal(0, 1), X1 = Z 2 1 + Z 2 2 + Z 2 3 + Z 2 4 , X2 = Z 2 1 + Z 2 2 + + Z 2 6 , X3 = Z 2 5 + Z 2 6 + + Z 2 10 and consider the following statements.

I. Z 2 1 + Z 2 2 + Z 2 3 2 3

II. X1/4 X2/6 F4,6

III. X1/4 X3/6 F4,6

IV. Z1 X1/4 t4 4

V. Z1 X3/6 t6

Which of the above statement(s) is/are correct?

(A) Only I and III.

(B) Only I, II, and III.

(C) Only II, III and V.

(D) Only I, II, III, IV, and V.

(E) None of the above