- Show Work When Possible Round Answers To Three Decimal Places And Include Units Where Possible Clearly Label Your Sol 1 (101.29 KiB) Viewed 153 times
Show work when possible. Round answers to three decimal places, and include units where possible. Clearly label your solutions. You may use your book or class note and you may work with others on the homework, but you must write your own copy. Point values appear in parentheses in front of each question. a 1. (2 points) Prove that MSE(Ô) = Var(ô) + Biascên)? 2. (2 points) Let X1, X2, ..., Xn be iid from Uniform(0,8] with pdf f(x) 1/B, where 0<x<B. (a) Find a method of moment estimator for B and call it ßmom (b) Verify the unbiasedness of Âmom 3. (2 points) Let X1, ..., Xn be a random sample from a gamma probability distribution with parameters a and B. Find (a) Moment estimators for the unknown parameters a and B. (b) MLEs for the unknown parameters a. 4. Let X1, ..., X, be a random sample from a population with probability density function f(x) = 0x8-1, 0<x<0. Show that T = 11-11; is sufficient for 6 5. (2 points) Let X1, ..., X, be a random sample from a population with probability density function f(2) ве 1 > 0. Find the lower bound of the variance of unbiased estimator for g(0) = 0 Hint: If X1, X2, ..., Xn is random sample from a population with probability density function f(x; 4) such that: • T = h(2) is unbiased estimator of g(@). • L(0) = II"=1 (2:0) then, the lower bound of the variance of unbiased estimator, V(T), for g(6) given by: [g(0) VT) > -a2 In L(0) EL ** n -or a82