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Imagine I want to randomly sample how fast a driver is going on a highway. And for this purpose, let's assume that the distribution is normal with the mean as the speed limit. Now if I take a sample, that would give me a single speed that a driver might be going. But what I'd like to do is repeatedly sample how fast one specific driver is going. My thought process is to first sample on the previously mentioned distribution to get that specific driver's average speed, $u_1$. Then perform many samplings on the new normal distribution with $\text{mean}=u_1$.

Please look at comments for a better example.

My feeling is that for repeated samples, each driver has their own individual mean, which the first sample gives us, and then further samples should be around that mean and not the global mean.

I feel like this is the right thing to do, but I can't express the idea well to get any hits on google. Is this the correct way to do this (and if so what's the name for this technique)?

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    This seems like a frequent sampling issue: use the global distribution to get the mean for the individual. Then sample on a new distribution around that sampled mean for specific instances. Is this a common statistical technique? If so what is it called? If not is there a better technique? This sounds intuitive to me, so I'm really looking for keywords or terms so I can research further. I just can't get my search started because I don't know the right names.2012-10-17

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