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GitHub #154 Description of VAR inconsistent

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I stated that the heights are equally probable, which they are not.
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Roger Labbe
2018-01-29 09:27:24 -08:00
parent 68ca5960cc
commit e8b88adf5f
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03-Gaussians.ipynb
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@@ -513,7 +513,7 @@
"\n",
"$$\\mathit{VAR}(X) = E[(X - \\mu)^2]$$\n",
"\n",
"Ignoring the squaring for a moment, you can see that the variance is the *expected value* for how much the sample space $X$ varies from the mean $\\mu:$ ($X-\\mu)$. I will explain the purpose of the squared term later. We have the formula for the expected value $E[X] = \\sum\\limits_{i=1}^n p_ix_i$, and we will assume that any height is equally probable, so we can substitute that into the equation above to get\n",
"Ignoring the squaring for a moment, you can see that the variance is the *expected value* for how much the sample space $X$ varies from the mean $\\mu:$ ($X-\\mu)$. I will explain the purpose of the squared term later. We have the formula for the expected value $E[X] = \\sum\\limits_{i=1}^n p_ix_i$ so we can substitute that into the equation above to get\n",
"\n",
"$$\\mathit{VAR}(X) = \\frac{1}{n}\\sum_{i=1}^n (x_i - \\mu)^2$$\n",
" \n",