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In a population with N-6 the values of y are 8, 3, 1, 11, 4, and 7. Draw all possible unordered sam ples of size 4 from this population without replacement. (i) Find P(s) for each sample point (ii) Find T, for each unit. (ii) Find the sampling distribution of v. (iv) Is y an unbiased estimator of ? Justify your answer. ()Is V(F)- (1- Justify your answer. 72 () Is r an unbiased estimator of s? Justify your answer.

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Given that N-6 and the values of y are 8,3,1,11,4 and 7 The population mean is Y-5.6667 and Population mean square is S2-13.46 Sr. No.Sample (s) bar-Eybar),2 0.00693889 2.77788889 0.84033889 0.69438889 2.50683889 0.02778889 0.11108889 1.17353889 0.44448889 3.36098889 0.84033889 0.02778889 3.67373889 0.34023889 0.00693889 p(s) bar (8,3,1,11) 0.06667 5.75 (8,3,1,4) 0.06667 4 (8,3,1,7) 0.06667 4.75 (8,3,11,4) 0.066676.5 (8,3,11,7) 0.06667 7.25 (8,3,4,7)0.06667 5.5 (8,1,11,4) 0.06667 (8,1,11,7) 0.06667 6.75 (8,1,4,7) 0.06667 5 (8,11,4,7) 0.066677.5 (3,1,11,4) 0.06667 4.75 (3,1,11,7) 0.066675.5 (3,1,4,7) 0.06667 3.75 (3,11,4,7) 0.06667 6.25 (1,11,4,7) 0.06667 5.75 20.91667 8.666667 10.91667 13.66667 10.91667 5.666667 19.33333 17.58333 10 8.333333 18.91667 19.66667 6.25 12.91667 18.25 13.46 6 8 10 12 13 14 15 Mean 5.6667 16.3333Above table gives list of all unordered samples of size 4, sampling distribution of mean, P(s). Also from above table it is clear that sample mean-is unbiased estimator of population mean Y. And sample mean square s2 is unbiased estimator of population mean square S2 Also agrees the formula Var( (1-ng-(1-6)-1346-1.12 and Var(j)=1.12 1.12 and Var() 1.12 Here

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