Let X1, . . . , Xn be independent Gamma(2, θ) random variables. The goal is to test H0 : θ = 2 ve...

Question

Question

Let X1, . . . , Xn be independent Gamma(2, θ) random variables. The goal is to test H0 : θ = 2 versus H1 : θ not equal to 2.

(1) Find the test statistic Λ.

(2) Derive the rejection region of the corresponding LRT

Answer 1

Answer #1

we Niu eguakeh 殴(b) FLE @c困 2 kn under Ho we reject Ho, ㄥ เจ็

Answer 2

Similar Homework Help Questions

Let X1, . . . , Xn ∼ Exp(θ) and consider the test for H0 :...

Let X1, . . . , Xn ∼ Exp(θ) and consider the test for H0 : θ ≥ θ_0 vs H1 : θ < θ_0. (a) Find the size-α LRT. With rejection region, R = {sample mean > c} where c will depend on a value from the χ ^2 df=2n distribution. (b) Find the appropriate value of c.
Suppose that X1, X2, ..., Xn are independent random variables (not iid) with densities ÍXi(z10,) -.2...

Suppose that X1, X2, ..., Xn are independent random variables (not iid) with densities ÍXi(z10,) -.2 e _ θ:/z1(z > 0), where θί 〉 0, for i = 1, 2, , n. (a) Derive the form of the likelihood ratio test (LRT) statistic for testing versuS H1: not Ho. You do not have to find the distribution of the likelihood ratio test (LRT) statistic under Ho- Just find the form of the statistic. (b) From your result in part (a),...
Let X1, . . . , Xn ∼ Exp(θ) and we wish to test H0 :...

Let X1, . . . , Xn ∼ Exp(θ) and we wish to test H0 : θ = θ_0 vs H1 : θ not= θ_0. Find the asymptotic LRT for this scenario.

Let X1, X2, . . . , Xn be a random sample of size n from...

Let X1, X2, . . . , Xn be a random sample of size n from a normal population with mean µX and variance σ ^2 . Let Y1, Y2, . . . , Ym be a random sample of size m from a normal population with mean µY and variance σ ^2 . Also, assume that these two random samples are independent. It is desired to test the following hypotheses H0 : σX = σY versus H1 : σX...
Let X1, . . . , Xn be independent Poisson(θ) random variables with parameter θ >...

Let X1, . . . , Xn be independent Poisson(θ) random variables with parameter θ > 0. (1) Find the Bayes estimator of θ for a Gamma(α, β) prior. (2) Find the MSE of the Bayes estimator.
Let X1, . . . , Xn be independent Beta(θ, 1) random variables with parameter θ...

Let X1, . . . , Xn be independent Beta(θ, 1) random variables with parameter θ > 0. (1) Find the Bayes estimator of θ for a Gamma(α, β) prior. (2) Find the MSE of the Bayes estimator.

Let X1, . . . , Xn ∼ Geo(θ), f(x)= θ(1-θ)^x, and we wish to test H0 : θ ≤ 1/3 vs H1 : θ > 1/3....

Let X1, . . . , Xn ∼ Geo(θ), f(x)= θ(1-θ)^x, and we wish to test H0 : θ ≤ 1/3 vs H1 : θ > 1/3. a) Using the full sample, X1....Xn, find the form of the UMP test for the hypotheses H0: θ=1/3 vs H1: θ=1/2. b)If n=15 and α = 0.1, what is the rejection region and the size of test in (a)?
Let X1, . . . , Xn ∼ Exp(θ) and we wish to test H0 : θ = θ_0 vs H1 : θ not= θ_0. Find the asympto...

Let X1, . . . , Xn ∼ Exp(θ) and we wish to test H0 : θ = θ_0 vs H1 : θ not= θ_0. Find the asymptotic LRT for this scenario.
Let X1, . . . , Xn ∼ Geo(θ), f(x)= θ(1-θ)^x, and we wish to test...

Let X1, . . . , Xn ∼ Geo(θ), f(x)= θ(1-θ)^x, and we wish to test H0 : θ ≤ 1/3 vs H1 : θ > 1/3. a) Using the full sample, X1....Xn, find the form of the UMP test for the hypotheses H0: θ=1/3 vs H1: θ=1/2. b)If n=15 and α = 0.1, what is the rejection region and the size of test in (a)?

Suppose X1, . . . , Xn be a random sample from the Beta(θ, 1) distribution. Find the P-value for the LRT test of the hypotheses H0 : θ ≥ 1 vs H1 : θ < 1.

Suppose X1, . . . , Xn be a random sample from the Beta(θ, 1) distribution. Find the P-value for the LRT test of the hypotheses H0 : θ ≥ 1 vs H1 : θ < 1.