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Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution. As this tag is ambiguous, please consider [survey-sampling] for the former and [monte-carlo] or [simulation] for the latter. For questions regarding creating random samples from known distributions, please consider using the [random-generation] tag.

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Distribution of the mean of distributions for samples with a given standard deviation

I have a normal distribution $N(0, \sigma^2)$. If I start selecting all distributions $N(\mu, \sigma^2/2)$ from this distribution, what are the parameters of the distribution for the mean $\mu$: $N(0, …
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