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.
for x > 0
The joint PDF of X_{1}, X_{2}, ..., X_{n} is, by independence is,
Let
Thus,
By Factorization theorem,
is sufficient statistic for θ
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