Q 9. The probability of including a speciedjnit in a sample of size 2 is 25. Q 10. Write the expression for population variance 02 and population mean square S2 and show their relationship. Q 11. Show that in simple random sampling wor, the sample mean 3.: is an un biased estimator of population mean Y, i.e E (y) = F and sampling variance for sample mean is given by ' l l 9 n 5'2 52 V = S": l = 1 _ (y) (M N) ( N)\" ( f)?I Q 12. In simple random sampling wor, write the expression of variance and standard error for sample total Q 13. Use the following small population of N=4 values and samples of size n=2 to verify that for SRS the sample mean, 37 , is an unbiased estimator of the population mean, 17, with standard error of [1 f ]S 2 , the standard symbolic notation is I! assumed. Population: [5, 9, 2, 10] Q 14. Signatures to a petition were collected on 700 sheets. Each sheet was provided with space of 50 signatures, but the signatories put their signatures in in erratic ways and the number of signatures per sheet was not definite. Twelve (12) sheets were spoiled in transit. Of the available sheets, a random sample of 50 sheets was drawn by SRS(WOR) and number of signatures per sheet counted, which are shown as below: Numberof 52 51 46 42 40 3? 32 29 27 15 14 10 signatures (Yi) -."\"""". Estimate the total number of signatures to the petition and calculate 95% confidence limit. Q 15. Show that, sample mean square is the unbiased estimate of population mean square, i.e