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