Question

Let X1,…, Xn be a sample of iid random variables with pdf f (x; ?) =...

Let X1,…, Xn be a sample of iid random variables with pdf f (x; ?) = 3x2 /(?3) on S = (0, ?) with Θ = ℝ+. Determine

i) a sufficient statistic for ?.

ii) F(x).

iii) f(n)(x)

Homework Answers

Answer #1

from part (iii)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X1,…, Xn be a sample of iid random variables with pdf f (x ∶ ?)...
Let X1,…, Xn be a sample of iid random variables with pdf f (x ∶ ?) = 1/? for x ∈ {1, 2,…, ?} and Θ = ℕ. Determine the MLE of ?.
Let X1,…, Xn be a sample of iid Exp(?1, ?2) random variables with common pdf f...
Let X1,…, Xn be a sample of iid Exp(?1, ?2) random variables with common pdf f (x; ?1, ?2) = (1/?1)e−(x−?2)/?1 for x > ?2 and Θ = ℝ × ℝ+. a) Show that S = (X(1), ∑ni=1 Xi ) is jointly sufficient for (?1, ?2). b) Determine the pdf of X(1). c) Determine E[X(1)]. d) Determine E[X2(1) ]. e ) Is X(1) an MSE-consistent estimator of ?2? f) Given S = (X(1), ∑ni=1 Xi )is a complete sufficient statistic...
Let X1, X2, . . . , Xn be iid random variables with pdf f(x|θ) =...
Let X1, X2, . . . , Xn be iid random variables with pdf f(x|θ) = θx^(θ−1) , 0 < x < 1, θ > 0. Is there an unbiased estimator of some function γ(θ), whose variance attains the Cramer-Rao lower bound?
Let X1, . . . , Xn be a random sample from the following pdf: f(x|θ)=...
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.
Let X1, ... , Xn be a sample of iid Beta(4, ?) random variables with ?...
Let X1, ... , Xn be a sample of iid Beta(4, ?) random variables with ? ∈ (0, ∞). a) Determine the likelihood function L(?). b) Use the Fisher–Neyman factorization theorem to determine a sufficient statistic S for ?.
Let X1, ... , Xn be a sample of iid Gamma(?, 1) random variables with ?...
Let X1, ... , Xn be a sample of iid Gamma(?, 1) random variables with ? ∈ (0, ∞). a) Determine the likelihood function L(?). b) Use the Fisher–Neyman factorization theorem to determine a sufficient statistic S for ?.
Let X1,…, Xn be a sample of iid N(0, ?)random variables with Θ = ℝ. a)...
Let X1,…, Xn be a sample of iid N(0, ?)random variables with Θ = ℝ. a) Show that T = (1/?)∑ni=1 Xi2 is a pivotal quantity. b) Determine an exact (1 − ?) × 100% confidence interval for ? based on T. c) Determine an exact (1 − ?) × 100% upper-bound confidence interval for ? based on T.
Let X1,…, Xn be a sample of iid Gamma(?, ?) random variables with ? known and...
Let X1,…, Xn be a sample of iid Gamma(?, ?) random variables with ? known and Θ=(0, ∞). Determine a) the MLE ? of ?. b) E(? ̂). c) Var(? ̂). e) whether or not ? is a UMVUE of ?.
Let X ∼ Geo(?) with Θ = [0,1]. a) Show that pdf of the random variable...
Let X ∼ Geo(?) with Θ = [0,1]. a) Show that pdf of the random variable X is in the one-parameter regular exponential family of distributions. b) If X1, ... , Xn is a sample of iid Geo(?) random variables with Θ = (0, 1), determine a complete minimal sufficient statistic for ?.
2 Let X1,…, Xn be a sample of iid NegBin(4, ?) random variables with Θ=[0, 1]....
2 Let X1,…, Xn be a sample of iid NegBin(4, ?) random variables with Θ=[0, 1]. Determine the MLE ? ̂ of ?.