3.16 (a)Why does the estimated correlation (3.19) always lie in the range (−1, 1)?

(b) Suppose the means y( jk)

j and y( jk)

k in the definitions of s( jk)

jj , s( jk)

jk , and s( jk)

kk in (3.17) are replaced by the means y( j)

j and y(k)

k from all available units for those variables. Is the resulting estimated correlation (3.19)

always in the range (−1, 1)? Either prove that it is or provide a counterexample.