Let X,..., Xn i.i.d. 2 Unif(a, 3), i.e., its pdf is f(x) = 1 B- if...

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Let X₁,..., Xn i.i.d. 2 Unif(a, 3), i.e., its pdf is f(x) = 1 B-α¹ if a < x < 3, else. (a) [50 points] Given that a is known, find a sufficient statistic for 3. (b) [40 points] Given that a is known, construct a sufficient and unbiased estimator for 3. (c) [20 points] Given that 3 is known, find a sufficient statistic for a. Let X₁,..., Xn i.i.d. 2 Unif(a, 3), i.e., its pdf is f(x) = 1 B-α¹ if a < x < 3, else. (a) [50 points] Given that a is known, find a sufficient statistic for 3. (b) [40 points] Given that a is known, construct a sufficient and unbiased estimator for 3. (c) [20 points] Given that 3 is known, find a sufficient statistic for a.