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Briefly describe two interpretations of probability. Justify the claim that the sample mean of a random variable is random itself. And say what are the

Briefly describe two interpretations of probability.

Justify the claim that "the sample mean of a random variable is random itself". And say what are the implications for statistical inference about this fact?

How can you argue that statistical analysis (confidence intervals etc) and hypothesis tests are valid and useful, even when the sample observations are not randomly selected?

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