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Let X w BIN(n, p) and - Mn. (a) Find a consistent c that (b) Find an impartial assessor ot Var(X). (c) Consider an arbitrary

Let X w BIN(n, p) and - Mn.

(a) Find a consistent c that

(b) Find an impartial assessor ot Var(X).

(c) Consider an arbitrary example ot size N trom BIN(n, p). Discover fair assessors ot p and Var(X)

in light of the irregular example.

58..

Assume X that is constant and its pdf, t(x; g), is symmetric about That is, influenza + c; u) =

c; g) peak all O.

(a) Show that peak an irregular example of size n, where n is odd (n = 2k 1) the example middle,

is a fair assessor ot u.

(b) Show that Z = Xl:n = u and W u = x mn nave a similar conveyance, and in this way that the

midrange, (Xl:n+ Xn.n)/2, is fair-minded peak g.

59..

Consider an irregular example ot size n trom a typical circulation, Xi NV, 9).

(a) Find the CRLB peak changes ot fair-minded assessors ot g.

(b) IS tne MLE, R, an IJMVIJEO%J?

(c) Is the MLE ottne 95th percentile an UMVLIE?

60..

An assessor

is supposed to be middle fair-minded it < > Considera irregular

test ot size n trom a remarkable dissemination, X, EXP(9)_

(a) Find a middle fair-minded assessor ot 9 that nas the torm =

(b) Find the relative proficiency ot contrasted with f.

(c) Compare the MSEsot and R when n = 5.

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