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small change in wording

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jonaslandsgesell committed Sep 10, 2019
1 parent 2e163bc commit 573602d6b5b8b09a91dd321693a25426e4f33c09
Showing with 2 additions and 2 deletions.
  1. +2 −2 doc/tutorials/12-constant_pH/12-constant_pH.ipynb
@@ -212,7 +212,7 @@
"but they do not have the same probability distribution as $X$. They are called _statistics_ because they are calculated\n",
"from a sample of the population, and can be used as _estimators_ of the moments $\\mu_\\alpha$ and $\\sigma_\\alpha$.\n",
"\n",
"According to the Central Limit Theorem (CLT), the probability distribution $\\sqrt{n}(\\bar{\\alpha} - \\mu_\\alpha)$ for large $n$ converges in probability distribution to $\\mathcal{N}(0, \\sigma_n^2)$. This statement can be rewritten as:\n",
"According to the Central Limit Theorem (CLT), the probability distribution $\\sqrt{n}(\\bar{\\alpha} - \\mu_\\alpha)$ for large $n$ converges to the probability distribution $\\mathcal{N}(0, \\sigma_n^2)$. This statement can be rewritten as:\n",
"\n",
"\\begin{equation}\n",
" z = \\frac{\\bar{\\alpha} - \\mu_\\alpha}{\\sigma_n} \\sqrt{n} \\sim \\mathcal{N}(0,1)\n",
@@ -235,7 +235,7 @@
"\\end{equation}\n",
"\n",
"To plot the simulated curve with error bars, we need to estimate three parameters: $\\mu_\\alpha$ and $w^\\pm$.\n",
"The accuracy of our estimation will depend on the sample size `num_samples`. The larger it is, the closer\n",
"The accuracy of our estimation will depend on the sample size `num_samples`. The larger it is, the more\n",
"$\\sqrt{n}(\\bar{\\alpha} - \\mu_\\alpha)$ converges to $\\mathcal{N}(0, \\sigma_n^2)$ and the smaller the $w^\\pm$ interval gets.\n",
"\n",
"The sample mean $\\bar{\\alpha}$ is already an unbiased estimator of $\\mu_\\alpha$.\n",

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