Question

Let X1, . . . , Xn ∼ iid N(θ, σ^2 ) for σ ^2 known....

Let X1, . . . , Xn ∼ iid N(θ, σ^2 ) for σ ^2 known. Find the UMP size-α test for H0 : θ ≥ θ0 vs H1 : θ < θ0.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X1, . . . , Xn ∼ iid Beta(θ, 1). (a) Find the UMP test...
Let X1, . . . , Xn ∼ iid Beta(θ, 1). (a) Find the UMP test for H0 : θ ≥ θ0 vs H1 : θ < θ0. (b) Find the corresponding Wald test. (c) How do these tests compare and which would you prefer?
Problem 2 Let X1, · · · , Xn IID∼ N(θ, θ) with θ > 0....
Problem 2 Let X1, · · · , Xn IID∼ N(θ, θ) with θ > 0. Find a pivotal quantity and use it to construct a confidence interval for θ.
4. Suppose that we have X1, · · · Xn iid∼ N(µ, σ2 ) (a) Derive...
4. Suppose that we have X1, · · · Xn iid∼ N(µ, σ2 ) (a) Derive a 100(1 − α)% confidence interval for σ 2 when µ is unknown. (b) Derive a α−test for σ 2 when hypotheses is given as: H0 : σ^2 = σ^2sub0 vs H1 : σ^2 < σ^2sub0 . where σ 2 0 > 0 and µ is unknown. I am particularly struggling with b. Part a I could do.
Suppose that X1,...,Xn are iid N(μ,σ2) where μ is unknown but σ is known.  μ>=2. Let z(μ)=μ3....
Suppose that X1,...,Xn are iid N(μ,σ2) where μ is unknown but σ is known.  μ>=2. Let z(μ)=μ3. Find an initial unbiased estimator T for z(μ). Next, derive the Rao-Blackwellized version of T.
Let X1, X2, · · · , Xn be a random sample from an exponential distribution...
Let X1, X2, · · · , Xn be a random sample from an exponential distribution f(x) = (1/θ)e^(−x/θ) for x ≥ 0. Show that likelihood ratio test of H0 : θ = θ0 against H1 : θ ≠ θ0 is based on the statistic n∑i=1 Xi.
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 ?.
Suppose that X1, X2, X3, X4 are iid N(θ,4). We wish to test H0: θ =...
Suppose that X1, X2, X3, X4 are iid N(θ,4). We wish to test H0: θ = 2 vs H1: θ = 5. Consider the following tests: Test 1: Reject H0 iff X1 > 4.7 Test 1: Reject H0 iff 1/3(X1 + 2X2) > 4.5 Test 3: Reject H0 iff 1/2(X1 + X3) > 4.2 Test 4: Reject H0 iff x̄>4.1 (xbar > 4.1) Find Type 1 and Type 2 error probabilities for each test and compare the tests.
Let X1, X2, …, Xn be iid with pdf ?(?|?) = ? −(?−?)? −? −(?−?) ,...
Let X1, X2, …, Xn be iid with pdf ?(?|?) = ? −(?−?)? −? −(?−?) , −∞ < ? < ∞. Find a C.S.S of θ
Suppose that X1,..Xn are iid N(0,σ2) where σ>0 is the unknown parameter. with preassigned α in...
Suppose that X1,..Xn are iid N(0,σ2) where σ>0 is the unknown parameter. with preassigned α in (0,1), derive a level α LR test for the null hypothesis H0: σ2 = σ02 against H1: σ2/=σ02 in the implementable form. (Hint: When is the function g(u) = ue1-u, u > 0 increasing? When is it decreasing? Is your test one-sided or two-sided?)
Problem 1 Let X1, · · · , Xn IID∼ p(x; θ) = 1/2 (1 +θx),...
Problem 1 Let X1, · · · , Xn IID∼ p(x; θ) = 1/2 (1 +θx), −1 < x < 1, −1 < θ < 1. 1. Estimate θ using the method of moments. 2. Show that the above MoM is consistent by showing it’s mean square error converges to 0 as n goes to infinity. 3. Find its asymptotic distribution.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT