soln1 - 1 ISyE 6739 Test#2 Solutions Summer 2005 This test...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 ISyE 6739 — Test #2 Solutions Summer 2005 This test is open notes, open books. You have exactly 90 minutes . Just do the best you can, and good luck! 1. (30 points) Short Answer Questions. (a) Suppose X has p.d.f. f ( x ) = 5 x 4 , 0 x 1. Find E [2 X - 5]. ANSWER: 2 E [ X ] - 5 = - 10 / 3. (b) If X again has p.d.f. f ( x ) = 5 x 4 , 0 x 1, find Var (2 X - 5). ANSWER: 4 Var ( X ) = 0 . 0793. (c) Suppose X can equal 1 or 2, each with probability 1 / 2. Find E [ n( X )]. ANSWER: 1 2 n(2) = 0 . 347. (d) TRUE or FALSE? E [ X 2 ] ( E [ X ]) 2 . ANSWER: True. (e) Suppose X has m.g.f. M X ( t ) = 0 . 3 e t + 0 . 7. What’s the distribution of X ? ANSWER: Bern(0.3). (f) If X has m.g.f. 4 / (4 - t ), for t < 4, find the m.g.f. of 2 X - 1. ANSWER: 4 e - t / (4 - 2 t ), t < 2. (g) TRUE or FALSE? If Cov ( X, Y ) = 0, then X and Y are independent. ANSWER: False.
Image of page 1

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

View Full Document Right Arrow Icon
2 (h) Suppose that X and Y are independent Exponential( λ ) random variables. What is the m.g.f. of X + Y ? ANSWER: ( λ/ ( λ - t )) 2 . (i) Suppose that X and Y are independent Exponential( λ ) random variables. Find Var ( XY ) (yup — the variance of the product).
Image of page 2
Image of page 3
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