Prove that MSE(@) = v(ô) + [Bias(@)]?
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- Suppose that: E(X) = - 38 (mu) / 35 and E(Y) = 11 (mu) Prove that the following are unbiased estimators of (mu), if not, calculate the bias: (mu.hat) = 6X + Ywhat happened to the 1(1-lambda) part in the first lineE(X) = - 38 (mu) / 35 and E(Y) = 11 (mu) Prove that the following are unbiased estimators of (mu), if not, calculate the bias: (mu.hat) = 6X + Y
- Consider the following bivariate time series model Xt = Wt, Yt = Wt + Wt-1+ Ut, where {w;} and {; } are standard (variance = 1) Gaussian white nosie and they are independent of each other. Show that (xt , Yt) are jointly weakly stationary.Suppose that @, and ô, are unbiased estimators of the parameter 0 and that V@,) = 15 and V(@2) = 4. What is the relative efficiency of the two estimators?If the alleles A and B of the cystic fibrosis gene occur in a population with frequencies p and 1 - p (where pis between 0 and 1), then the frequency of heterozygous carriers (carriers with both alleles) is 2p(l - p). Which value of p gives the largest frequency of heterozygous carriers?
- This is a problem using the empirical ruleA student attempted to use L’Hopital’s Rule as follows. Did the student make an error, if any, or does it state “no error”?We know that the point estimator o` is an unbiased estimator for the parameter 0 if E(e') = 0.If the estimator is biased (not unbiased), then the difference E(O) – 0 is called the bias of the estimator e and is denoted by Bias(e'). That is,