Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    5
    ReputationRep:
    Hi, I need help with this statistics question - any help is much appreciated. Thank you !!
    Attached Images
     
    Offline

    22
    ReputationRep:
    (Original post by Nazzy_HCrest)
    Hi, I need help with this statistics question - any help is much appreciated. Thank you !!
    What have you tried?
    • Thread Starter
    Offline

    5
    ReputationRep:
    (Original post by Zacken)
    What have you tried?
    Thing is I have to go over the lecture notes in order to answer ir but the deadline is tomorrow at 4pm and I have other assignments I need to complete. So I was hoping for a solution - even if it is for one part
    Offline

    13
    ReputationRep:
    (Original post by Nazzy_HCrest)
    Thing is I have to go over the lecture notes in order to answer ir but the deadline is tomorrow at 4pm and I have other assignments I need to complete. So I was hoping for a solution - even if it is for one part
    Trouble is the rules of the forum do not allow for complete solutions...So, to get you started,

    (i) You are given the probability distribution, therefore you can simply write down the likelihood function for n independent observations. It is

    \displaystyle L(\phi) = \prod_{i=1}^{n} \frac{2y_i}{\phi} \exp\left({\frac{-y_{i}^{2}}{\phi}}\right)

    Now use standard mathods to find the MLE. In this case, the logarithm of the likelihood is easier to work with.

    (ii) In your notes you should have a theorem about the asymptotic distribution of the MLE - it involves the Fisher information of one observation. This is a straightforward application of that theorem,

    (iii) Remember what a pivot is: a function of  \phi and the observations whose distribution is independent of  \phi . (Remember how subtracting the mean and dividing by the standard deviation converts an arbitrary normal random variable into a standard normal random variable that is independent of  \mu and  \sigma ). Your asymptotic pivot should drop straight out of part (ii).

    (iv) Standard manipulation of probability distributions.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brussels sprouts
    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

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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