Problem 1 If and 2 are unbiased estimators of the same parameter 0, what condition must be imposed on the constants k and k so that 2k101 + 2k202 is also an unbiased estimator of 0? Prove your assertion. Problem 2 = Suppose E(3)13. Is an unbiased estimator of ? Explain. If not, find an estima- tor that is unbiased for 3. Problem 3 Let X1, X2, X, have the pdf f(x|0) = 0x0-1 for 0 x1 and > 0. Derive the method of moments (MOM) estimator for . [Hint: You will first need to calculate E(X) via integration!] Problem 4 Let X1,..., Xn be iid from Exponential(A) with pdf f(x) = Ae. Derive the MLE for >.