Question

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?

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 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.
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.
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.
Let X1, X2, …, Xn be iid with pdf ?(?|?) = ? −(?−?)? −? −(?−?) ,...
Let X1, X2, …, Xn be iid with pdf ?(?|?) = ? −(?−?)? −? −(?−?) , −∞ < ? < ∞. Find a C.S.S of θ
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∼iid Gamma(3,1/θ) and we assume the prior for θ is InvGamma(10,2). (a) Find the posterior...
Let X1,...,Xn∼iid Gamma(3,1/θ) and we assume the prior for θ is InvGamma(10,2). (a) Find the posterior distribution for θ. (b) If n= 10 and   ̄x= 18.2, find the Bayes estimate under squared error loss. (c) The variance of the data distribution is φ= 3θ2. Find the Bayes estimator (under squared error loss) for φ.Let X1,...,Xn∼iid Gamma(3,1/θ) and we assume the prior for θ is InvGamma(10,2). (a) Find the posterior distribution for θ. (b) If n= 10 and   ̄x= 18.2, find...
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 ?.
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.
Let X1,…, Xn be a sample of iid U[?, 1] random variables with Θ = (−∞,...
Let X1,…, Xn be a sample of iid U[?, 1] random variables with Θ = (−∞, 1]. a) Show that T = (1−X(1) )/(1−?) 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, 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?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT