# Bayesian Distribution of Sample Mean

Bayesian Distribution of Sample Mean

This Demonstration provides Bayesian estimates of the posterior distribution of the mean and the standard deviation of a normally distributed random variable . These posterior distributions are based upon observing independent observations of the random variable that have sample mean and sample distribution . Prior knowledge about statistical parameters is an important part of Bayesian statistics. In this case, it is initially assumed that the unknown mean is uniformly distributed on the interval <μ< and that the unknown standard deviation is distributed with a Jeffrey's prior distribution on the interval <σ<. Bayes's theorem provides a convenient way of incorporating the prior information and the observed information into a posterior probabilistic characterization of the unknown parameters and .

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