P Set 7 - Problem Set 7 MGTECON 603 2009 MGTECON 603...

Info icon This preview shows pages 1–2. Sign up to view the full content.

Problem Set 7, MGTECON 603, 2009 1 MGTECON 603, Econometrics I Jules H. van Binsbergen Fall 2009 Stanford GSB PROBLEM SET 7 Due: Monday November 30 th 1. Let the random variable X have probability density function f X ( x ; θ ) = (1 ) exp( x/θ ) for x > 0. Consider the simple hypothesis H 0 : θ = 2 and the alternative hypothesis H 1 : θ = 4. Let X 1 , X 2 denote a random sample of size two from this distribution. Show that the best test of H 0 against H 1 may be carried out by use of the statistic X 1 + X 2 . Find the optimal critical region for α = 0 . 1. 2. Let X 1 , . . . , X 10 be a random sample of size 10 from a normal distribution with mean zero and variance σ 2 . Find a best critical region for testing H 0 : σ 2 = 1 against H 1 : σ 2 = 2 of size α = 0 . 05. Is this also a best test of the same null hypothesis against the alternative hypothesis H 1 : σ 2 = 3? And against the alternative hypothesis H 1 : σ 2 > 1? 3. Let X 1 , X 2 , . . . , X N be a random sample from a distribution with pdf f X ( x ; θ ) = θx θ - 1 for 0 < x < 1. Find the form of the best critical region for testing
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern