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Confidence interval

  1. Jul 16, 2013 #1
    1. The problem statement, all variables and given/known data

    Let θ>0 and X1, X2,...,Xn be a random sample from the distribution with the pdf

    fx(x)=fx(x;θ)=(θ/(2√x))e-θ√x, x>0

    Recall:
    Ʃ√xi, i=1, n has Gamma (α = n, "usual θ" = 1/θ) distribution.

    a) Suggest a confidence interval θ with (1-α)100% confidence level.

    b) Suppose n = 5, x1=5, x2=11, x3=2, x4=7, x5=3. Use part (a) to construct at 95% confidence interval for θ.

    2. Relevant equations



    3. The attempt at a solution

    attempting to mimic what my professor did on a similar problem..

    a)
    303enlw.png

    b)
    2mhxxz9.png

    So

    1) Is my work correct?
    2) I don't understand why Ʃ√xi is relevant here
    3) I don't understand the relationship between gamma and chi2 distributions

    Appreciate it.
     
  2. jcsd
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