Question: 2. Consider a random sample X1, ..., X, from the Bernoulli distribution with success proba- bility 0 (that is, the Binomial(1, 0) distribution). (a) Show

2. Consider a random sample X1, ..., X, from the Bernoulli

2. Consider a random sample X1, ..., X, from the Bernoulli distribution with success proba- bility 0 (that is, the Binomial(1, 0) distribution). (a) Show that S? = En(X; -X)?/(n-1) is unbiased for 0(1 -0), where X = EN, Xi. (b) We know that Var($2) = n(n - 1)2 n20 - 5n202 + 12n02 - 2n0 + 8n203 - 20n03 +0-702 +1203-604 + 10n04 - 4n204). Does S' attain the Cramer-Rao lower bound

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