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Suppose you have two (or more) normal distributions with different mean and variance.

You can draw only one sample of only one of the available distributions. Your goal is to get the biggest value possible.

How do you choose, in a systematic way, which one of the distribution is the rational choice?

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Simply find the distribution which has a mean significantly bigger than the rest. Sampling from this distribution will give you the biggest value in expectation.

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  • $\begingroup$ I don't think that, for instance, a big mean with a big variance would grant the optimum result. Maybe, the answer is finding the expected value for all the distributions and choosing the greater like in stats.stackexchange.com/questions/176702/… ? $\endgroup$ – Robert Jan 4 at 13:20
  • $\begingroup$ The expected value of a normal distribution is its mean, regardless of the variance. Consequently, if distribution A has a greater mean than distribution B, samples drawn from A will be greater than samples drawn from B, in expectation. $\endgroup$ – bi_scholar Jan 4 at 13:40

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