can someone help me answer these? i give 5 stars for accurate answers, someone sent me wrong answers and solution

TRUE or FALSE. Determine whether the following statements are true or false. If the statement is true, provide a one sentence explanation or calculations as to why it is true. Otherwise, provide any counterexample when the statement is false. a. An estimator O with a variance equal to the Cramer-Rao lower bound is the UMVUE for d. b. Given X1, X2, . .., X'n is a random sample from a Poi()) distribution, then only knowing X1, the first observation is enough to give us an unbiased estimator for A. c. Given X1, X2, . .., Xn is a random sample from a Ber(p) distribution, we say that the sample mean X, is a more efficient estimator for p than the mean of a subset of the sample X,-k for any k > 0. d. The Rao-Blackwellized estimator T" is always going to have a lower variance than the original estimator T. e. If the UMVUE exists, it is always the BLUE