Let x1, x2, ...,X, be a random sample from N(u, o?), and let 0 = (6x1 - 2x2) -(4x3-3x4) %3D | 4 be an estimator of the parameter u, calculate the bias of this estimator.
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- Let X1,...,Xn be an iid sample from f(x | θ) = θ xθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θLet X1, . . . , Xn be an iid sample from f(x | θ) = θxθ−1 , 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ.Let X1,...,Xn be an iid sample from f(x | θ) = θxθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
- Let X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameterFind the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln (1-U), where U ~ U (0,1) and λ> 0.
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