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Math · Statistics And Probability
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6. Suppose that X1, X2, X3, is a random sample from a N(μ, θ) distribution, where the mean μ and the variance θ are unknown parameters. Let X be the sample mean and S2 be the sample variance. Also let W-Σ(x(i+1)-X(i))2/S2. (a) Find the sufficient statistics for (μ, θ). Is it complete? (b) Are X and S2 independent? Justify. (c) Show that W is independent of (X, S2).

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