thank you Problem 2. For Example 7.7 in text (Page 335), show that(1). E(Ô,)= 0,02(2). Var(ê)п(п + 2)02(3). Var(@2)3n We argued in Example 7.5 that when X1, ..., X, is a random sample from a uniformdistribution on [0, 0], the estimatorExample 7.7п+1max(X1, ..., X„)nis unbiased for 0 (we previously denoted this estimator by 04). This is not the onlyunbiased estimator of 0. The expected value of a uniformly distributed rv is just themidpoint of the interval of positive density, so E(X;) = 0/2. This implies thatE(X) = 0/2, from which E(2X) = 0. That is, the estimator Ô2If X is uniformly distributed on the interval [A, B], then V(X) = o(Exercise 23 in Chapter 4). Thus, in our situation, V(X;) = 0²/12, V(X)o2/n = 0 /(12n), and V(Ô2) = V(2X) = 4V(X) = 0² /(3n). The results of Exercise50 can be used to show that V(01)= 0²/[n(n+2)]. The estimator 0, has smallervariance than does 02 if 3n < n(n + 2)–that is, if 0 < n² – n = n(n – 1). As long asn > 1, V(01) < V(02), so 01 is a better estimator than 02. More advanced methodscan be used to show that 0, is the MVUE of 0-every other unbiased estimator of 0has variance that exceeds 0 /[n(n + 2)].= 2X is unbiased for 0.(B -A)/12

Name: thank you Problem 2. For Example 7.7 in text (Page 335), show that(1).
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Description: thank you Problem 2. For Example 7.7 in text (Page 335), show that(1). E(Ô,)= 0,02(2). Var(ê)п(п + 2)02(3). Var(@2)3n We argued in Example 7.5 that when X1, ..., X, is a random sample from a uniformdistribution on [0, 0], the estimatorExample 7.7п+1m