# Stats problem – ex.9.73 and 9.87

Stats problem – ex.9.73 and 9.87

Stats problem – ex.9.73 and 9.87

9.73 An urn contains 0 black balls and N – 0 white balls. A sample of n balls is to be selected without
replacement. Let Y denote the number of black balls in the sample. Show that (N/n) Y is the method of moments estimator for 0.

9.87 A random sample of 100 voters selected from a large population revealed 30 favoring candidate A, 38 favoring candidate B, and 32 favoring candidate C. Find MLEs for the proportions of voters in the
population favoring candidates A, B, and C, respectively. Estimate the difference between the
franctions favoring A and B and place a 2-standard-deviation bound on the error of estimation.

Stats problem – ex.9.73 and 9.87

9.73 An urn contains 0 black balls and N – 0 white balls. A sample of n balls is to be selected without
replacement. Let Y denote the number of black balls in the sample. Show that (N/n) Y is the method of moments estimator for 0.

9.87 A random sample of 100 voters selected from a large population revealed 30 favoring candidate A, 38 favoring candidate B, and 32 favoring candidate C. Find MLEs for the proportions of voters in the
population favoring candidates A, B, and C, respectively. Estimate the difference between the
franctions favoring A and B and place a 2-standard-deviation bound on the error of estimation.