Question

Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with...

Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with -∞<μ<∞ and σ2 > 0.

a. Develop a likelihood ratio test for H0: μ <= μ0 vs. H1: μ > μ0

b. Develop a likelihood ratio test for H0: μ >= μ0 vs. H1: μ < μ0

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

Homework Answers

Answer #1

Solution:

Given that....

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
If (x1, . . . , xn) is a sample from an N(μ0, σ2) distribution, where...
If (x1, . . . , xn) is a sample from an N(μ0, σ2) distribution, where σ2 > 0 is unknown and μ0 is known a.determine the MLE of σ2. b. show that the mle of σ2 is asymptotically normal
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.
X1, · · · Xn ~ iid N(µ, σ2 ) (a) Derive a 100(1 − α)%...
X1, · · · Xn ~ iid N(µ, σ2 ) (a) Derive a 100(1 − α)% confidence interval for σ2 when µ is unknown. (b) Derive a α−test for σ2 when H0 : σ2 = σ02  vs H1 : σ2 < σ02  Where σ02 > 0 and µ is unknown.
Let X1, …,Xn be a random sample from f(x; θ) = θ exp(-xθ) , x>0. Use...
Let X1, …,Xn be a random sample from f(x; θ) = θ exp(-xθ) , x>0. Use the likelihood ratio test to determine test H0 θ=1 against H1 θ ≠ 1.
Let X1,..., Xn be a random sample from the Rayleigh distribution: Use the likelihood ratio test...
Let X1,..., Xn be a random sample from the Rayleigh distribution: Use the likelihood ratio test to give a form of test (without specifying the value of the critical value) for H0: θ= 1 versus H1:≠1
Let X1,..., Xn be a random sample from the Geometric distribution: Use the likelihood ratio test...
Let X1,..., Xn be a random sample from the Geometric distribution: Use the likelihood ratio test to give a form of test (without specifying the value of the critical value) for H0: p= 1 versus H1:p≠1
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.
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?)
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∼iid N(μ,σ2). a) Suppose that μ is known. What is the MLE of...
Suppose that X1,..., Xn∼iid N(μ,σ2). a) Suppose that μ is known. What is the MLE of σ? (b) Suppose that σ is known. What is the MLE of μ? (c) Suppose that σ is known, and μ has a prior distribution that is normal with known mean and variance μ0 and σ02. Find the posterior distribution of μ given the data.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT