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Co-authored-by: Jeremy Cohen <jcohen02@users.noreply.github.com>
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"1. We are taking 2000 samples of a random variable X, those samples has some mean $m$ and standard deviation $\\sigma_X$, the mean is the center of mass of the above histogram and the standard deviation is a measure of how wide it is.\n",
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"2. However, what we actually want to do is ask \"How close is the mean to 0?\", to answer that we need to know how much we expect the mean to vary by when we rerun the calculation. Turns the mean of N samples of a variable X then the mean varies by \n",
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"2. However, what we actually want to do is ask \"How close is the mean to 0?\", to answer that we need to know how much we expect the mean to vary by when we rerun the calculation. It turns out that given N samples of a variable X, the mean varies by \n",
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" $$\\sigma_m = \\sigma_X / \\sqrt{N}$$\n",
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" this is usually called the standard error of the mean.\n",
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"\n",
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