4. Prove Theorem 2. [Hint: For any real and (> 0) compute the PDF of...

4. Prove Theorem 2. [Hint: For any real μ and σ (> 0) compute the PDF of

(U(r)

−μ)/σ and show that the standardized U(r), (U(r)

−μ)/σ, is asymptotically N(0,1) under the conditions of the theorem.]