I'm wondering what theorem I should use here. Please solve this question with all processes and detailed explanations. Thanks!

1. A manufacturer of skateboard wheels purchases ball bearing from their supplier in 2 kg and 4kg containers. The quality of the ball bearings in n 2kg containers and m 4kg containers were assessed to ensure that they meet the necessary specication for man- ufacturing wheels. Let the independent random variables X1, . . .,Xn and 1/1,. . . ,Ym denote the number of faulty ball bearings in the 2kg and 4kg containers respectively, where X1- ~ Pois(2/\\) (for i = 1, . . . ,n) and Y3- ~ Pois(4/\\) (for j = 1, . . . , m). The follow- ing two estimators have been proposed to estimate the population rate parameter A for the number of faulty ball bearings per kilogram: X T1=+ 3 22+? 8 where X = zzll X1- and l7 = % 22:1 Yj denote the sample mean estimator for the 2 kg and 4kg containers respectively. Show that both estimators are unbiased in estimating A and derive an expression for their standard error. Under what circumstances (i.e. the relationship between H. and m) will make the estimator T1 more efcient than estimator T2 in estimating A