Question

3. Let Xi, . . . , Xn be iid randoln variables with mean μ and variance σ2. Let, X denote the sample mean and V-Σ, (X,-X)2. (a) Derive the expected values of X and V. (b) Further suppose that Xi,-.,X, are normally distributed. Let Anxn ((a)) an orthogonal matrix whose first rOw 1S be , ..*) and iet Y = AX, where Y (Yİ, ,%), ard X-(XI, , X.), are (column) vectors. (It is not necessary to know aij for i-2,...,n,j-1,..., n for answering the following questions.) (i) Find Σ-i aii for i 1, , n and show that Σηί Y2-Σί, 1Xi. (Use properties of orthogonal matrices.) (ii) Express X and V in terms (or as functions) of Yi,... , Y, (iii) Use (only) transformation of variables approach to find the joint distribution of Yi,... ,Yn Are Yi,..., Yn independently distributed and what are their marginal distri- butions (iv) Prove that X and V are independently distributed and give their marginal distri- butions

0 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
3. Let Xi, . . . , Xn be iid randoln variables with mean μ and...
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