95% Confidence Interval for λConsider a random sample X 1 , X 2 , . . , X n from a variable with density function f X ( x ) = 2 λ π x e − λ π x 2 x &gt; 0A useful estimator of λ is λ ^ = n π ∑ i = 1 n X 1 2 Derive a 95% confidence interval for λ (a hint is provided suggesting to consider the distribution of λ λ ^ ) .).

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95% Confidence Interval for   λConsider a random sample       X    1    ,      X    2    ,  .  .  ,      X    n   from a variable with density function      f    X    (  x  )  =  2  λ  π  x      e          −      λ      π              x        2                                   x  &amp;gt;  0A useful estimator of   λ is            λ      ^        =      n          π              ∑                  i          =          1                          n                            X        1        2            Derive a 95% confidence interval for   λ (a hint is provided suggesting to consider the distribution of       λ                  λ        ^                        )        .).

Abram Jacobson · Accepted Answer

Step 1You can take the corresponding quantiles for the Gamma distribution and proceed similarly as if the distribution was normal - let Z be Gamma distributed.Step 2Then you have:      P    (  Z  ∈  (      q                  α        2              ,      q          1      −                        α          2                      )  )  =  1  −  αwhere       q                  α        2              ,      q          1      −                        α          2                     are the corresponding quantiles

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