Let X1,..., Xm and Y1,..., Yn be samples from N(, 2) and N(, 2). Then T

Let X1,..., Xm and Y1,..., Yn be samples from N(ξ, σ2) and N(ξ, τ 2). Then T = (

 Xi,

Yj,

 X2 i ,

Y 2 j ), which in Example 4.3.3 was seen not to be complete, is also not boundedly complete.

[Let f (t) be 1 or −1 as y¯ − ¯x is positive or not.]