Q.Consider two-factor anova model with no interaction . Each cell have only one observation,

yij = ?+ ?i + ?j+ eij , eij~N (0, ?^2 ) ,i = 1 , 2 , ... .a,j = 1 , 2 , ... b.

( 1 ) Show that the number of Iinearly independent estimable functions is ( a+b - 1 )

( 2) Find a basis set of these estimable functions.

(3) The linear Combination ?ci?i is estimable iff ?ci = 0

( 4) The best unbiased estimator of ?ci?i is ?ci?i.

( 5 ) Find the UMVU estimator of ?^2 (use exponential family)

Q. Consider two-factor anova model with no interaction . Each cell have only one observation . yij = M+ di+ Bj+ eij , eij lian ( o , 6 2 ) i = 1 , 2 , ...,a j = 1 , 2 , .1- 3 b ( i) Show that the number of linearly independent estimable functions is ( at 6 - 1 ) . (ii) Find a basis set of these estimable functions (fii) The linear Combination I cidi is estimable iff Zci = 0 ( iv ) The best unbiased estimator of Ecidi is SGyi . ( v) the UMVU estimator of oz -= 55 ( 41) - 4:.- 4.,+7) j=1 14 ( a - 1) ( 6 -1 )