A gamma density is x⁴e^(−x/β)/(24β⁵),x>0,β>0. For β=2,find the Cramér–Rao lower bound for variance of an unbiased estimator of β² from n=8 observations,to one decimal.
The gamma shape is 5,so one observation carries information 5/β²;the sample information is 40/β². For g(β)=β²,the bound is [g′(β)]²/I=4β²/(40/β²)=β⁴/10. At β=2,this is **1.6**.
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