2. This question concerns the proof of the CramerRao lower bound (CRLB) as presented in lecture videos. One particular aspect of the proof that is referenced here are the three claims numbered \"1.", "2." and \"3.\" that are established in the proof in sequence. These will be referred to below as \"the three claims" for brevity. (a) [TYPE] Write down the three claims using only English words. Do not use any formulae. Do not use any mathematical symbols. [3] (b) [TYPE:] For each of the three claims. decide whether the assumption that E[T(X)] = 6 is used in establishing this claim. If you decide that it is used, describe which part of the proof of the claim makes use of this assumption. [3] (c) Let X N N((6,6)T,I) be bivariate normal with both marginal means equal to the parameter 9 E (9 = IR and covariance matrix equal to the identity matrix. For each of the following expressions, decide whether it is (i) a statistic, (ii) an unbiased estimator of 0 and justify your decisions. ii. X1 iii. % ((X1 a)? + (X2 0)?) iv. 9 [4] (d) Let Y ~ N((61,62)T, ( Orig \"155,29 D where 01,02 > 0 and g 6 (1,1) hold. Compute the Fisher information [(6) on 6 = (61,62)T contained in Y, de- cide whether 1(6) is positive definite symmetric and justify Your decision. [TYPE] Provide an interpretation of the dependence of 1(0) on 01. [5]