Assignment 4 - Stat 5101(Geyer Fall 2009 Homework...

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

View Full Document Right Arrow Icon
Stat 5101 (Geyer) Fall 2009 Homework Assignment 4 Due Wednesday, October 7, 2009 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 4-1. If U , V , X , and Y are any random variables, show that cov( U + V, X + Y ) = cov( U, X ) + cov( V, X ) + cov( U, Y ) + cov( V, Y ) 4-2. Suppose X 1 , X 2 , X 3 are IID with mean μ and variance σ 2 . Calculate the mean vector and variance matrix of the random vector Y = Y 1 Y 2 Y 3 = X 1 - X 2 X 2 - X 3 X 3 - X 1 4-3. Suppose X and Y are independent random variables, with means μ X and μ Y , respectively, and variances σ 2 X and σ 2 Y , respectively. Calculate E ( X 2 Y 2 ) in terms of μ X , μ Y , σ 2 X , and σ 2 Y . 4-4. Suppose 6 balls that are indistinguishable except for color are placed in an urn and suppose 3 balls are red and 3 are white. Suppose 2 balls are drawn. What is the probability the one is red and the other white under each of the following conditions?
Image of page 1

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

View Full Document Right Arrow Icon
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