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Plug-in estimates: Unbiased estimates are not transformation invariant, Show that: a.) In N(?, ?2), x?2 is not...

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Basic Math

Plug-in estimates: Unbiased estimates are not transformationinvariant, Show that:

a.) In N(?, ?2), x?2 is not an unbiasedestimate of ?2

b.) In Exponential(?), e^(-x? ) is not an unbiased estimate of?.

c.) In Poisson(?), e^(-x? ) is not an unbiased estimate ofe^?.

d.) s is not an unbiased estimate of ?

Answer & Explanation Solved by verified expert
4.5 Ratings (756 Votes)
If then is an unbiased estimator of aHere we haveLet n be the sample size SoSo x2    See Answer
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