Suppose independent observations are made for three populations, , and .
Moreover, there is fair temporal correlation between the two independent observations giving credence to both data records.
In a sense, there is no true risk because you have a sum of many independent observations with a left bound on the outcome.
Later that day, the discovery was confirmed by independent observations.
A large number of independent observations will be necessary before either generalization can be justified.
Any dispute will be settled when independent observations are able to conclude whether or not the machine works in the way it is claimed.
It is an unstructured corpus of independent observations which rarely go beyond what seems to have happened in the past.
If we have independent observations in a sample and is the estimated correlation for .
We are also asking for free elections under independent international observation.
The sample size, n, for independent observations in this case is one, not two.