Question: Question 3 (22 total points) Let X1, X2, - -- ,Xn be an iid random sample from a beta distribution and it's probability density function

density function given by I'(a + )3) f ('1') = none And

also, 3(a) = is and W) = m ma'la'l for00,>0 Answer the

following questions using the above ilaformation. (a) (2 points) Find the expected

Question 3 (22 total points) Let X1, X2, - -- ,Xn be an iid random sample from a beta distribution and it's probability density function given by I'(a + )3) f ('1') = none And also, 3(a) = is and W) = m ma'la'l for00,>0 Answer the following questions using the above ilaformation. (a) (2 points) Find the expected value of :E, 13(5). (b) (4 points) Find the variance value of 5:, V(:). (c) (4 points) Show that r is a biased estimator of atB 6 (d) (4 points) Find the Bias of x, B(x) when i is the estimator of .(e) (6 points) Find MSE(x) when x is the estimator of 1 atB . (f) (2 points) Propose an unbiased estimator of atB

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