Based on 'Explaining the Gibbs sampler', C. Casella and E.I. George, Amer. Statist. 46 (3) (1992), 167-174. Histogram (cf. Fig. 1)) t Obs Exp Diff Ratio Comp of X2 0 25 23 2 1.050 0.060 1 35 40 -5 0.873 0.649 2 46 50 -4 0.918 0.340 3 62 55 7 1.126 0.880 4 58 55 3 1.038 0.079 5 61 53 8 1.137 1.003 6 41 49 -8 0.833 1.364 7 37 43 -6 0.856 0.902 8 47 36 11 1.288 3.028 9 26 29 -3 0.882 0.412 10 19 22 -3 0.837 0.604 11 16 16 0 0.969 0.016 12 14 11 3 1.252 0.711 13 8 6 2 1.163 0.182 14 4 3 1 1.085 0.027 15 1 1 0 0.636 0.208 16 0 0 0 0.000 0.418 Chi-squared equals 10.883 on 16 degrees of freedom Estimated densities (cf. Fig. 3) t Obs Exp Diff Ratio Comp of X2 0 25 23 2 1.050 0.060 1 40 40 0 0.997 0.000 2 49 50 -1 0.978 0.025 3 53 55 -2 0.963 0.076 4 54 55 -1 0.966 0.065 5 51 53 -2 0.950 0.132 6 47 49 -2 0.955 0.098 7 42 43 -1 0.971 0.036 8 35 36 -1 0.959 0.061 9 29 29 0 0.984 0.008 10 22 22 0 0.969 0.022 11 17 16 1 1.030 0.014 12 12 11 1 1.073 0.060 13 8 6 2 1.163 0.182 14 4 3 1 1.085 0.027 15 2 1 1 1.272 0.116 16 0 0 0 0.000 0.418 Chi-squared equals 1.399 on 16 degrees of freedom. Histogram (n random) t Obs Histogram 0 26 ************************** 1 41 ***************************************** 2 52 **************************************************** 3 55 ******************************************************* 4 61 ************************************************************* 5 54 ****************************************************** 6 38 ************************************** 7 41 ***************************************** 8 30 ****************************** 9 26 ************************** 10 25 ************************* 11 14 ************** 12 11 *********** 13 11 *********** 14 9 ********* 15 2 ** 16 0 17 0 18 2 ** 19 0 20 1 * 21 0 Estimated densities (n random; cf. Fig. 5) t Obs Estimate 0 21 ********************* 1 41 ***************************************** 2 51 *************************************************** 3 55 ******************************************************* 4 54 ****************************************************** 5 51 *************************************************** 6 46 ********************************************** 7 40 **************************************** 8 34 ********************************** 9 28 **************************** 10 21 ********************* 11 16 **************** 12 11 *********** 13 8 ******** 14 5 ***** 15 3 *** 16 2 ** 17 1 * 18 0 19 0 20 0 21 0