Q7. Let X; (i = 1,.,n) be a random sample from the N(u, o²) population with unknownparameters u and o?. Then we know that T, = E-1(X - X)²/(n – 1) is an unbiased estimator-xi-1 . Now consider two other estimators T, and T3 for o? whereof a? and further,(n-1)TT2 = E(X – X)*/n and T3 = E(X – X)²/n + 1).%3DWhat is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s.Show that among the three estimators T,, T2 and T3 the one with minimum m.s.e. is T3.

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Let X, (i 1,.,n) be a random sample from the N(4,02) population with unknown ameters u and o2. Then we know that T, = E-1(X-X)²/(n – 1) is an unbiased estimator 3? and further, = 2(X- X) /n and T, = E(X-X)/(n + 1). (n-1)T ~xỉ-1. Now consider two other estimators T2 and T3 for o? where %3D at is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s.

Let X, (i 1,.,n) be a random sample from the N(4,02) population with unknown ameters u and o2. Then we know that T, = E-1(X-X)²/(n – 1) is an unbiased estimator 3? and further, = 2(X- X) /n and T, = E(X-X)/(n + 1). (n-1)T ~xỉ-1. Now consider two other estimators T2 and T3 for o? where %3D at is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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