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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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Probably.
    It is not trivial that the distribution is a Gaussian distribution, but it is true here.
     
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