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
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