Thank you mute, all you said seems very right and true to me. with large enough mu compared to sigma it will become pretty normal. I might have to use some other distribution to pick the variance if i use this for something. But this was more of a though experiment.
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...