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Merge pull request #168 from fubel/patch-1

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Typo correction
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Roger Labbe 2017-08-27 14:07:38 -04:00 committed by GitHub
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Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb
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@ -598,7 +598,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"This is what we expected. The input is the Gaussian $\\mathcal{N}(\\mu=1, \\sigma=1.4)$, and the function is $f(x) = 2x+1$. Therefore we expect the mean to be shifted to $f(\\mu) = 2*1+12=14$. We can see from the plot and the print statement that this is what happened. \n",
"This is what we expected. The input is the Gaussian $\\mathcal{N}(\\mu=1, \\sigma=1.4)$, and the function is $f(x) = 2x+12$. Therefore we expect the mean to be shifted to $f(\\mu) = 2*1+12=14$. We can see from the plot and the print statement that this is what happened. \n",
"\n",
"Before I go on, can you explain what happened to the standard deviation? You may have thought that the new $\\sigma$ should be passed through $f(x)$ like so $2(1.4) + 12=14.81$. But that is not correct - the standard deviation is only affected by the multiplicative factor, not the shift. If you think about that for a moment you will see it makes sense. We multiply our samples by 2, so they are twice as spread out as before. Standard deviation is a measure of how spread out things are, so it should also double. It doesn't matter if we then shift that distribution 12 places, or 12 million for that matter - the spread is still twice the input data.\n",
"\n"