7. Suppose X₁ and X₂ are independent N(μ, 1) random variables, for an unknown parameter μ. (a) Find a sufficient statistic for u. (b) Show that X – 1 is an unbiased estimator of μ². (c) Find a MVUE estimator of μ². You may use the fact that X₁|(X₁ + X₂ = y) ~ N (1,¹).

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