Turn on thread page Beta

Very difficult STATISTICS question. watch

Announcements
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hello there,
    it is the third time I have come across a question like this and I still have no idea how to do such a question.

    It is quite long and I would be very very appreciative of help!!

    The question is as follows:

    "Let x_1, x_2, ..., x_n be arandom sample from a population described by a normal distribution with mean M ('mew'), and variance σ², and y_1, y_2,..., y_m be a random sample from another population described by a normal distribition with mean 2M (2 'mew') and variance σ². Write down the combined log likelihood from both samples. Determine the maximum likelihood estimates of the parameters M and σ² (give the MLE of σ² in terms of the MLE of M). Determine the matrix of -1xthe second derivatives of the log-likelihood function ll(M,σ²) evaluated at these estimates. Hence determine an approximate 99% confidence interval for M."

    Thank you very much for your time.
    Offline

    8
    ReputationRep:
    Please see the attachments.

    Writing v rather than \sigma^2 makes the solution neater.
    Attached Images
      
    Offline

    8
    ReputationRep:
    Please see the attachments.

    Writing v rather than \sigma^2 makes the solution neater.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: December 6, 2005

University open days

  • University of Lincoln
    Brayford Campus Undergraduate
    Wed, 12 Dec '18
  • Bournemouth University
    Midwifery Open Day at Portsmouth Campus Undergraduate
    Wed, 12 Dec '18
  • Buckinghamshire New University
    All undergraduate Undergraduate
    Wed, 12 Dec '18
Poll
Do you like exams?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.