Question

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

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 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
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.
Suppose X1, · · · , Xn from a normal distribution N(µ, σ2 ) where µ...
Suppose X1, · · · , Xn from a normal distribution N(µ, σ2 ) where µ is unknown but σ is known. Consider the following hypothesis testing problem: H0 : µ = µ0 vs. Ha : µ > µ0 Prove that the decision rule is that we reject H0 if X¯ − µ0 σ/√ n > Z(1 − α), where α is the significant level, and show that this is equivalent to rejecting H0 if µ0 is less than the...
Suppose X1, . . . , Xn are a random sample from a N(0, σ^2) distribution....
Suppose X1, . . . , Xn are a random sample from a N(0, σ^2) distribution. Find the MLE of σ^2 and show that it is an unbiased efficient estimator.
Let X1,...,Xn be a random sample from a normal distribution where the variance is known and...
Let X1,...,Xn be a random sample from a normal distribution where the variance is known and the mean is unknown.   Find the minimum variance unbiased estimator of the mean. Justify all your steps.
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?)
Let X1, . . . , Xn be a random sample from a Poisson distribution. (a)...
Let X1, . . . , Xn be a random sample from a Poisson distribution. (a) Prove that Pn i=1 Xi is a sufficient statistic for λ. (b) The MLE for λ in a Poisson distribution is X. Use this fact and the result of part (a) to argue that the MLE is also a sufficient statistic for λ.
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, . . . , Xn be a random sample from a Bernoulli(θ) distribution, θ...
Let X1, . . . , Xn be a random sample from a Bernoulli(θ) distribution, θ ∈ [0, 1]. Find the MLE of the odds ratio, defined by θ/(1 − θ) and derive its asymptotic distribution.
Suppose that X1,..., Xn form a random sample from the uniform distribution on the interval [0,θ],...
Suppose that X1,..., Xn form a random sample from the uniform distribution on the interval [0,θ], where the value of the parameter θ is unknown (θ>0). (1)What is the maximum likelihood estimator of θ? (2)Is this estimator unbiased? (Indeed, show that it underestimates the parameter.)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT