Theory of Estimation

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A random sample x1, x2, x3, x4, x5 of size 5 is drawn from a normal population with unknown mean. Consider the following estimators to estimate mean.

(i) t1=(x1+x2+x3+x4+x5)/5

(ii) t2=(x1+x2)/2+x3

(iii) t3=(2x1+x2+Kx3)/3


Q1. find K

Q2. are t1 and t2 unbiased?

Q3. which is the most efficient estimator?

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