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5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show th...

5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/

1.(c)
2.(a),(b)

-e λ , X > 0 2) (x 1. Let Xi, , Xn be a random sample from exponential distribution with (a) Find a complete and sufficient s

5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/n x"-'e-x/θ , x > 0.0 > 0 6. Let Xi, ,Xn be i.i.d. gamma(α,6) where α > l is known. ( f(x) Γ(α)θα (a) Show that Σ X, is complete and sufficient for θ (b) Find ElI/X] (c) Find the UMVUE of 1/0
-e λ , X > 0 2) (x 1. Let Xi, , Xn be a random sample from exponential distribution with (a) Find a complete and sufficient statistic for (b) Find an unbiased estimator of 2 based only on X (c) Find a better unbiased estimator than the one in part (b) λ. , X, be iid N(μ, σ2). Let θ-u'ay 2. Let Xi, (a) Show that (X, S2) is a complete sufficient statistic (b) Find the UMVUE of μ/σ
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