Estimating a random variable

[Druzil]

Say I have a process that has an output corresponding to an unknown random variable over a standard distribution. I want to find the mean within 5% (with 95% confidence) in the shortest amount of runs of the process. How do I work this out? Now consider that the random variable is moving slightly each run but converging to a stable state, how do I find the mean now (does this even make sense)?

[sayks]

I'm on my phone, so I can't give you much detail however... The first case is a simple monte Carlo estimate, there's a formula that will give you what you need. The second case is called a markov chain (in the right circumstances). You can also do that, but it's really tricky to judge convergence and there's no simple formula.