Question

You have an observation x from N(o,σ). Decide c so that c|x| is a unbiased estimation...

You have an observation x from N(o,σ). Decide c so that c|x| is a unbiased estimation of σ and calculate the estimations variance. Answer exactly.

please explain thoroughly.
thank you in advance. :)

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Answer #1

Given,

where x is a single observation from the normal population

To find,
An unbiased estimator of using x

we know,

the unbiased estimator of is,
                                                       

we know that the mean of the population is 0,

thus an unbiased estimator of ,
                                                       

Checking,


                

Required which would be the unbiased estimator of .

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