Consider the following Bayesian model for the stratied sampling data in Problem 2 for each stratum a" = 1, 2: 'd . 1/13.?- Iiu'iao-I? 32" N(Hiao-i2) for 3:1321'HIM1'; 'd analog\": NONE/nu}; .9 I612. 5) . 2 0:: where no : 0.0001 and b is set to be equal to the unbiased estimator of the population variance you computed in Problem 2. 5 Write a BUGS-style program (either in OpenBUGS or in JAGS or in RJAGS) for the above model. Please email your program to bingling@ucla.edu b Compute the posterior estimates (mean, median and 95% credible intervals) for the total number of inhabitants in the 64 cities. > Also present posterior estimates (mean, median and 95% credible intervals) for the total number of inhabitants in each stratum. The table below presents data from one of the rst stratied sampling exercises in the United States carried out in 1920 to estimate the number of inhabitants in the Mpop = 64 largest cities of the time. These 64 cities were divided into N = 2 strata, where the rst strata comprised M1 = 16 of the largest cities and the second strata comprised the remaining M 2 = 48 cities. Within the rst stratum m1 = 6 cities were chosen, while m2 = 18 cities were chosen from stratum 2. The total number of inhabitants, in thousands, for each of these 24 cities is given in the table. Stratum 1 Stratum 2 324 180 130 101 797 314 172 121 507 238 153 116 748 296 163 119 457 235 138 113 381 192 132 104 Table: Inhabitants, in thousands, from a stratied random sample of 24 US cities. p Provide an unbiased estimate of the total number of inhabitants in the 64 largest cities of the US in 1920. b Provide an estimate of the variance of the above estimator