The variance of the estimate X1 of θ1 is σ2 if we use the first experiment. But if we use the second experiment, the variance of the estimate given above is σ2/8. Thus the second experiment gives us 8 times as much precision for the estimate of a single item, and estimates all items simultaneously, with the same precision. What the second experiment achieves with eight would require 64 weighings if the items are weighed separately. However, note that the estimates for the items obtained in the second experiment have errors that correlate with each other.
The va.riance of the estimate X1 of θ1 is σ2 if we use the first experiment But if we use the second experiment, the variance of .the estimate given above is σ2/8. Thus the second experiment gives us 8 times as much precision for the estimate of a single item, and estimates all items simultaneously, with the same precision What the second experiment achieves with eight would require 64 weighings if the items are weighed separately. However, note that the estimates for the items obtained in the second experiment have errors that correlate with each other.