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Let X1, . . . , Xn be a random sample from the following pdf: f(x|θ)=...

  1. Let X1, . . . , Xn be a random sample from the following pdf:


    f(x|θ)= (x/θ)*e^(-x^2/2θ). x>0

    (a) Find a sufficient statistic for θ.

Math   Statistics-And-Probability   
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Answer #1

for x > 0

The joint PDF of X1, X2, ..., Xn is, by independence is,

Let

Thus,

By Factorization theorem,

is sufficient statistic for θ

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