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Suppose that

`x_(1),x_(2),dots,x_(n)`

are i.i.d.

`N(\mu ,\sigma ^(2))`

. a. If

`\mu `

is known, what is the mle of

`\sigma `

? b. If

`\sigma `

is known, what is the mle of

`\mu `

? c. In the case above (

`\sigma `

known), does any other unbiased estimate of

`\mu `

have smaller variance?