Question: If X1 X2 Xn constitute a
If X1, X2, . . . , Xn constitute a random sample from a normal population with µ = 0, show that
Is an unbiased estimator of σ2.
Answer to relevant QuestionsIf X is a random variable having the binomial distribution with the parameters n and θ, show that n ∙ X/n ∙ (1 – X/n) is a biased estimator of the variance of X. Show that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter θ. With reference to Exercise 10.23, find the efficiency of the estimator with ω = 1/2 relative to the estimator with ω = n1/ n1 + n2. Show that if Θ is a biased estimator of θ, then If X1, X2, . . . , Xn constitute a random sample of size n from an exponential population, show that is a sufficient estimator of the parameter θ.
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