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## bayes formula and picking variance from distribution

This should be rather simple bayesian problem, but I can't figure it out for myself.

If i pick numbers from normal distributionS, where the variance of the distribution at each pick v1, is in turn picked out of a normal distribution with variance v2.

What is then the distribution of the random number? i tried this on my calculator a bit, and it looks as if it is normal itself, but what is the variance of x?

This is not homework, but something I would like to understand how to calculate.

//Cal