Let X be a random variable with mean and variance 2, and let X1, X2, , Xn be a random sample of size n from X Show that the statistic V k (Xi 1 Xi)2is an unbiased estimator for 2 for an appropriate choice for the constant k Find this value for k

Question: Let X be a random variable with mean and variance 2, and let X1, X2, , Xn be a random sample of size n from

Let X be a random variable with mean μ and variance σ2, and let X1, X2, , Xn be a random sample of size n from X. Show that the statistic V = k Σ (Xi+1 – Xi)2is an unbiased estimator for σ2 for an appropriate choice for the constant k. Find this value for k.

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