Assume that X,..., X, is a sample from the U(0, 0+1) distribution, and that it is desired to test Ho: 00 versus H,: 0 >

Assume that X₁,..., X, is a sample from the U(0, 0+1) distribution, and that it is desired to test Ho: 0≤0 versus H,: 0 > 0. Defining t₁ =min{x;} and t2 = max{x}, show that

(112)

is a UMP test of size a.

[0 if t₁<1-a1/n and t₂<1, 1 otherwise.