Steel rods in a large batch have lengths with mean and variance . Two trainees are...

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Steel rods in a large batch have lengths with mean and variance ². Two trainees are set the task of estimating u. Trainees A and B take random samples of 20 rods and 5 rods, respectively. Based on these samples, Trainee A calculates the mean length to be X, and Trainee B calculates the mean length to be X. However, the trainees decide they may get a better estimate by combining their individual estimates. They consider two different estimators: -X₁ (a) Are these estimators of μ unbiased? Show your work. (b) Calculate the bias and variance of these estimators. Which estimator is more efficient? Steel rods in a large batch have lengths with mean and variance ². Two trainees are set the task of estimating u. Trainees A and B take random samples of 20 rods and 5 rods, respectively. Based on these samples, Trainee A calculates the mean length to be X, and Trainee B calculates the mean length to be X. However, the trainees decide they may get a better estimate by combining their individual estimates. They consider two different estimators: -X₁ (a) Are these estimators of μ unbiased? Show your work. (b) Calculate the bias and variance of these estimators. Which estimator is more efficient?