Components of variance: Consider the hierarchical model where 1 ,..., m , 2 iid normal(, 2 ) y 1,j ,...,y n j ,j j , 2 iid normal( j , 2 ) For this problem, we will eventually compute the following: Var[y i,j j , 2 ],Var[ y ,j j , 2 ],Cov[y i 1 ,j ,y i 2 ,j j , 2 ] Var[y i,j , 2 ],Var[ y ,j , 2 ],Cov[y i 1 ,j ,y i 2 ,j , 2 ] First let's use our intuition to guess at the answers: (a) Which do you think is bigger, Var[y i,j j , 2 ] or Var[y i,j , 2 ] ? To guide your intuition, you can interpret the first as the variability of the Y's when sampling from a fixed group, and the second as the variability in first sampling a group, then sampling a unit from within the group. (b) Do you think Cov[y i 1