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Boole inequality and calculation of union probability of n arbitrary events. Explain in a simple way the concept of sampling distribution of the mean (or any other computable statistics on the sample as standard deviation (sigma) or mode or median)

Boole inequality and calculation of union probability of n arbitrary events. Explain in a simple way the concept of sampling distribution of the mean (or any other computable statistics on the sample as standard deviation (sigma) or mode or median)