7.60 Let Xi, of 1/β. , xn be iid gamma(α, β) with α known. Find the...
Let X1,…Xn ~ iid Gamma (α, θ) where the α is known and interested in the rate parameter θ, and we chosen a prior θ~ Gamma (3, 1). Find the posterior distribution
1.(c) 2.(a),(b) 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...
Let Xi, known , xn be a random sample from a gamna(α, β) distribution. Find the MLE of β, assuming α s
Let X1, , Xn be a random sample gamma(α, β), assume a is known. Consider testing Ho : β-A-Derive the Score test for testing Ho- Let X1, , Xn be a random sample gamma(α, β), assume a is known. Consider testing Ho : β-A-Derive the Score test for testing Ho-
Let X1 ,……, Xn be a random sample from a Gamma(α,β) distribution, α> 0; β> 0. Show that T = (∑n i=1 Xi, ∏ n i=1 Xi) is complete and sufficient for (α, β).
Let Xi,..., Xn be iid random variables with distribution Bern(p) (a) Is the statistic 름 Σ. ? (b) Is the statistic (Σ¡X 2? Xi an unbiased estimator of p i) an unbiased estimator of p Let Xi,..., Xn be iid random variables with distribution Bern(p) (a) Is the statistic 름 Σ. ? (b) Is the statistic (Σ¡X 2? Xi an unbiased estimator of p i) an unbiased estimator of p
Let X1,X2,...,Xn be iid exponential random variables with unknown mean β. (b) Find the maximum likelihood estimator of β. (c) Determine whether the maximum likelihood estimator is unbiased for β. (d) Find the mean squared error of the maximum likelihood estimator of β. (e) Find the Cramer-Rao lower bound for the variances of unbiased estimators of β. (f) What is the UMVUE (uniformly minimum variance unbiased estimator) of β? What is your reason? (g) Determine the asymptotic distribution of the...
Suppose that Xi, X2, ....Xn is an iid sample from where θ 0 is unknown. (a) Find the uniformly minimum variance unbiased estimator (UM VUE) of (b) Find the uniformly most powerful (UMP) test of versuS where θο is known. (c) Derive an expression for the power function of the test in part (b) Suppose that Xi, X2, ....Xn is an iid sample from where θ 0 is unknown. (a) Find the uniformly minimum variance unbiased estimator (UM VUE) of...
Let Y1,…,Yn~iid Gamma(5,β). Recall that Γ(5) = 4! a) Find the MLE for β. b) Is your answer to a) the MVUE? Use two methods to verify that it is unbiased.
Let X1, ,Xn be a random sample gamma(α, β), assume a is known. Consider testing Ho : β = βο. Derive Wald statistic for testing Ho using the MLE of B both in the numerator and denominator of the statistic. Let X1, ,Xn be a random sample gamma(α, β), assume a is known. Consider testing Ho : β = βο. Derive Wald statistic for testing Ho using the MLE of B both in the numerator and denominator of the statistic.