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Exercise2.16 An annualnumberofearthquakesinacertainseismicallyactiveregionisdistributed Poisson withanunknownmean . Let Y1, ...,Yn be thenumberofearthquakesintheareaduringthe last n years (itispossibletoassumethatthe Yi are

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Exercise2.16 An annualnumberofearthquakesinacertainseismicallyactiveregionisdistributed Poisson withanunknownmean λ. Let Y1, ...,Yn be thenumberofearthquakesintheareaduringthe last n years (itispossibletoassumethatthe Yi are independent).

1. Find theMLE ˆλ for λ.

2. Is ˆλ unbiased?

3. Does ˆλ achievetheCramer–Raolowerbound?

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