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Risk function

  1. Jul 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Let X1,X2 be a random sample of size 2, from a normal distribution with mean μ and σ2=1. Let T=t(X1,X2)=X1+X2 be the estimator of μ and l(t;μ)=t-μ be the loss function. Compute risk function R(μ).

    2. Relevant equations
    R(μ)=∫∫(l(t;μ))∏f(xi;μ)dxi


    3. The attempt at a solution
    Since we have a normal distribution, then

    ∏f(xi;μ)=(1/2∏)exp(-1/2)[(x1-μ)2+(x2-μ)2]

    l(t;μ)=t-μ=(X1+X2)-μ

    so the risk function is given by,

    R(μ)=∫∫[(X1+X2)-μ](1/2∏)exp(-1/2)[(x1-μ)2+(x2-μ)2]dx1dx2

    i just want to know if my equation for risk function is correct.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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