ZuoTi.Pro
Question

Step 2b: Deriving the Method of Moments Estimator 1 point possible (graded) We use the same set-up from the previous problems

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

From\ CLT, \ \bar{X}\to N(\mu, Var(\bar{X})=\frac{\sigma^{2}}{n}) \\ where\ \sigma : population\ std.dev\ . In\ our\ case\ population\ std.dev\\ is\ std.dev\ of\ Exp(\lambda^{*})\ which\ is\ = \frac{1}{\lambda^{*}} \\ So,\ Now\ here\ we\ want\ Var(\sqrt{n}(\bar{X}-\mu)) \ where\ \mu=1/\lambda^{*} \\ so \ we\ know\ Var(\sqrt{n}(\bar{X}-\mu))) = nVar(\bar{X})=n*\sigma^{2}/n = \sigma^2 = (1/\lambda^{*})^{2} \\ so\ in\ their\ notation\ \sigma^{2} = Var(\sqrt{n}(\bar{X}-\mu))) = (1/\lambda^{*})^{2}

0 0
Add a comment
Know the answer?
Add Answer to:
Step 2b: Deriving the Method of Moments Estimator 1 point possible (graded) We use the same...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • Concept Question: Maximum Likelihood Estimator for the Laplace distribution 1 point possible (graded) As in the...

    Concept Question: Maximum Likelihood Estimator for the Laplace distribution 1 point possible (graded) As in the previous problem, let mn MLE denote the MLE for an unknown parameter m* of a Laplace distribution. MLE Can we apply the theorem for the asymptotic normality of the MLE to mn? (You must choose the correct answer that also has the correct explanation.) No, because the log-likelihood is not concave. No, because the log-likelihood is not twice-differentiable, so the Fisher information does not...

  • Relating M-estimation and Maximum Likelihood Estimation 1 point possible (graded) Let (E,{Pθ}θ∈Θ) denote a discrete statistical...

    Relating M-estimation and Maximum Likelihood Estimation 1 point possible (graded) Let (E,{Pθ}θ∈Θ) denote a discrete statistical model and let X1,…,Xn∼iidPθ∗ denote the associated statistical experiment, where θ∗ is the true, unknown parameter. Suppose that Pθ has a probability mass function given by pθ. Let θˆMLEn denote the maximum likelihood estimator for θ∗. The maximum likelihood estimator can be expressed as an M-estimator– that is, θˆMLEn=argminθ∈Θ1n∑i=1nρ(Xi,θ) for some function ρ. Which of the following represents the correct choice of the function...

  • 2. Biased and unbiased estimation for variance of Bernoulli variables A Bookmark this page 2 points...

    2. Biased and unbiased estimation for variance of Bernoulli variables A Bookmark this page 2 points possible (graded) Let X1, X, bed. Bernoull random variables, with unknown parameter PE (0,1). The aim of this exercise is to estimate the common variance of the X First, recall what Var (X) is for Bernoulli random variables. Var (X) - Let X, be the sample average of the Xi. X. - 3x Interested in finding an estimator for Var(X), and propose to use...

  • photos for each question are all in a row (1 point) In the following questions, use...

    photos for each question are all in a row (1 point) In the following questions, use the normal distribution to find a confidence interval for a difference in proportions pu - P2 given the relevant sample results. Give the best point estimate for p. - P2, the margin of error, and the confidence interval. Assume the results come from random samples. Give your answers to 4 decimal places. 300. Use 1. A 80% interval for pı - P2 given that...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT