Question 1 Suppose we have I samples (each of size J): X1, X2, . .. , XI, taken from each of I possibly different populations. All observations are independent, inside and between the samples. The table below shows information of each samples Observation in EX] Var (X) X Sample Each Sample X11, X12, . . ., XIJ X1. X2 X21, X22, . . . , X2J 02 X2. S X3 X31, X32, . . . , X3J 02 X3. S . . .. . . . . . . . XI1, X12, . . . , XIJ HI o XI. Now assume that /1 = /2 = . . . = MI. (a) Show JEi(X1. - X.. )2 0 2 ~X 1_1), where X., is the sample mean of the sample means X. = Eil XI. (b) Show (J-1)21 5. ~ xi( J-1) (c) Show 1-1 JEi ( X 1 . - X.. )2 (J-1) Zi=1 S; ~ F( 1-1,1(J-1)) I ( J - 1 ) (d) Show Ell E,(Xij - X )? = Ell E,(Xij - X1.)? + El, J( X1. - X.. )2