Consider a Normal population with mean ๐œ‡ and variance ๐œŽ 2 < โˆž . We collect a sample of ๐‘‡ = 3 independent and identically distributed observations ๐‘ฅ = ( 7 , 10 , 4 ) In class we have shown that the standardized log-likelihood of the sample for this case is 1 ๐‘‡ log ( ๐ฟ ( ๐‘ฅ , ๐œ‡ , ๐œŽ 2 ) ) = โˆ’ 1 2 log ( 2 ๐œ‹ ) โˆ’ 1 2 log ( ๐œŽ 2 ) โˆ’ 1 ๐‘‡ โˆ‘ ๐‘ก = 1 ๐‘‡ ( ๐‘ฅ ๐‘ก โˆ’ ๐œ‡ ) 2 2 ๐œŽ 2 . Then the Maximum Likelihood estimate of the variance ๐œŽ 2 is: Single choice

A

๐œŽ ฬ‚ 2 = 6 .

B

There is not enough information to compute the value of ๐œŽ ฬ‚ 2 .

C

๐œŽ ฬ‚ 2 = 8 .

D

๐œŽ ฬ‚ 2 = 9 .

E

๐œŽ ฬ‚ 2 = 15 .

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