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# Very difficult STATISTICS question. watch

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1. 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.

Writing v rather than makes the solution neater.
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Writing v rather than makes the solution neater.

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Updated: December 6, 2005
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