Let X be a random variable with mean [tex]\mu[/tex] and standard deviation 1.(adsbygoogle = window.adsbygoogle || []).push({});

Let's add a twist.

Suppose [tex]\mu[/tex] is randomly distributed about 0 with standard deviation 1.

At each iteration, we select a new [tex]\mu[/tex] according to its distributuion. This mean is then used in the distribution for X. Then we pick an X according to its distribution.

My question: What is the resulting joint distribution? Given this joint distribution, I should be able to calculate the mean and standard deviation. Clearly, the mean X will be 0, but what will be the standard deviation of X? It seems that it should, at a minimum, be greater than 1.

Thanks!

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# Joint Distribution of Changing Mean

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