Suppose that a single observation X is taken from the uniform distribution on the interval [0, ],

Question:

Suppose that a single observation X is taken from the uniform on the interval [0, θ], where the value of θ is unknown, and the following simple hypotheses are to be tested:
H0: θ = 1,
H1: θ = 2.
a. Show that there exists a test procedure for which α(δ) = 0 and β(δ) < 1.
b. Among all test procedures for which α(δ) = 0, find the one for which β(δ) is a minimum.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...