Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: e) f) g) where k> 0 is a constant. f(x; λ) = 2-kxk-1e (k-1)! 0, if x > 0 elsewhere Justify whether or not  is a uniform minimum variance unbiased estimator of λ. Check whether or not the MLE of λ is a consistent. Suggest with a Fisher's factorization theorem, the sufficient estimator of 1.

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