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The value of E( (||X-μ||-c)^2 )

  1. Mar 28, 2008 #1
    I would like to ask one more question.

    X ~ N (μ, σ2)

    If X = [x1 x2] and μ = [μ1 μ2]. What is the value of E( (||X- μ||-c)^2 )?

    where c is constant and E(||X- μ||^2)= σ2


    Thank ...
     
  2. jcsd
  3. Mar 28, 2008 #2
    [tex]\mathbb{E}[ (||X- \mu||-c)^2 ]=\mathbb{E}[ ||X- \mu||^2-2c||X-\mu||+c^2 ][/tex]

    Now [itex]\mathbb{E}[\cdot][/itex] is linear ... does this help?
     
  4. Mar 29, 2008 #3
    Thank Pere Callahan. But I still don't know how to find E(||X- μ||) as I ask in https://www.physicsforums.com/showthread.php?t=224947 [Broken]

    Do you know how to find E(||X- μ||)?

    Thank you.
     
    Last edited by a moderator: May 3, 2017
  5. Mar 29, 2008 #4
    Did yu try to use the defintion of the expected value of some function g of a real random Variable X with density function f?
    [tex]
    \mathbb{E}[g(X)]=\int_{\mathbb{R}}{g(x)f(x)dx}
    [/tex]

    You will have to solve some Gaussian-type integrals but it should be straight-forward :smile:
     
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