Question

I1. Follow the steps below to show that the pooled estimator $p is an unbi- ased estimator for the common standard deviation of two independent sam ples Let Yi, Yi2, ..., Yini denote the random sample of size n from the first population with population mean μ| and population variance σ, and let Y21, Y22, ..., Y2na denote an independent random sample of size n2 from the second population with population mean μ2 and population mean ơ3. Sup- pose that σ,-σ2-σ. Then the pooled estimator S, is an unbiased estima- tor for the common variance σ2, where where Ý, the sample mean for the first sample and y2 is the sample mean for the second population. Complete the following steps: (a) Rewrite S2 in terms of Si and S2, where Si is the sample variance of the first population and S2 is the sample variance of the second populations (b) Use the result of Example 8.1 to show that E -σ2 (easily).

0 0
Add a comment Improve this question Transcribed image text
Answer #1

a> Note thar S is the Sample vamanee fun the Is sample and S2 is he somple vamanee for rhe 2nd sanple ni ni-1に! n 2 ni N oW 2

Add a comment
Know the answer?
Add Answer to:
I1. Follow the steps below to show that the pooled estimator $p is an unbi- ased...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

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
  • Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the...

    Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the same variance σ. Let sỈ and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled is an unbiased estimator of σ2

  • I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2...

    I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.

  • I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2...

    I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2

  • Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with...

    Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with the same variance σ2. Let s' and s denote the sample variances from two samples with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator (m-1)sit (n2-1)d ni t n22 pooled is an unbiased estimator of σ2

  • 3. You have two independent random samples: XiXX from a population with mean In and variance σ2 a...

    3. You have two independent random samples: XiXX from a population with mean In and variance σ2 and Y, Y2, , , , , Y,n from a population with mean μ2 and variance σ2. Note that the two populations share a common variance. The two sample variances are Si for the first sample and Si for the second. We know that each of these is an unbiased estimator of the common population variance σ2, we also know that both of...

  • Please give detailed steps. Thank you. 5. Let {X1, X2,..., Xn) denote a random sample of...

    Please give detailed steps. Thank you. 5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...

  • QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution,...

    QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...

  • 10.41] To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider...

    10.41] To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the finite variance σ2, we first take a random sample of size n. Then, we randomly draw one of n slips of paper numbered from 1 through n, and if the number we draw is 2, 3, ..., orn, we use as our estimator the mean of the random sample; otherwise, we...

  • Please show all work in a clear manner. Thank you so much in advance! Exercise 1...

    Please show all work in a clear manner. Thank you so much in advance! Exercise 1 Let X and S2 denote the sample mean and sample variance of an independent random sample of size 10 from N(0, σ*). Find c so that 〈 c | = 0.95.

  • To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the...

    To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the finite variance σ 2 , we first take a random sample of size n . Then, we randomly draw one of n slips of paper numbered from 1 through n , and • if the number we draw is 2, 3, ··· , or n , we use as our estimator the...

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