Central Limit Theorem.ipynb

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   "source": [
    "The [central limit theorem (CLT)](https://en.wikipedia.org/wiki/Central_limit_theorem) establishes that, when independent random variables are added, their properly normalized sum (and therefore their mean) tends toward a normal distribution even if the original variables themselves are not normally distributed.\n",
    "\n",
    "Here we just take mean value of $n$ samples over $m$ trials using various different distributions."
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   "metadata": {},
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   "source": [
    "using Distributions, Statistics, Plots"
   ]
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  {
   "cell_type": "code",
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     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "dists = [Normal(), Beta(), Gamma(), Poisson(), Exponential(), LogNormal()]\n",
    "n = 50    # Num samples to obtain mean\n",
    "m = 1000  # Number of sample means\n",
    "\n",
    "means = [[mean([rand(dist) for i in 1:n]) for j in 1:m] for dist in dists]\n",
    "\n",
    "histogram(means, layout=length(dists), leg=:none)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Here we see convergence to a normal distrubution "
   ]
  }
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