1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Statistics expected values problem

  1. Nov 21, 2015 #1
    1. The problem statement, all variables and given/known data
    1. Let X1 and X2 be independent normal random variables, distributed as N(μ1,σ^2) and N(μ2,σ^2), respectively. Consider a random variable U = 2X1 − X2.

      (a) Find the mean of U.
      (b) Find the variance of U.
      (c) Find the distribution of U.

    3. The attempt at a solution
    a) E(U) = 2E(X1) - E(X2) = 2μ1 - μ2

    b) Var(U) = 2^2 Var(X1) + (-1)^2 Var(X2)
    = 4σ^2 + σ^2 = 5σ^2
    c) This part I am not really sure what they are asking. Do they just want me to write N(2μ1 - μ2, 5σ^2) like they did for the other ones?
  2. jcsd
  3. Nov 21, 2015 #2


    User Avatar
    2017 Award

    Staff: Mentor

    It is not trivial that the distribution is a Gaussian distribution, but it is true here.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted