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Merge pull request #269 from rummanwaqar/master

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Bug fix: Issues in Chap 3 and 4
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Roger Labbe 2018-12-20 08:01:35 -08:00 committed by GitHub
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4
03-Gaussians.ipynb
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@ -313,7 +313,7 @@
"\n",
"If $x$ is continuous we substitute the sum for an integral, like so\n",
"\n",
"$$\\mathbb E[X] = \\int_{a}^b\\, f(x) \\,dx$$\n",
"$$\\mathbb E[X] = \\int_{a}^b\\, xf(x) \\,dx$$\n",
"\n",
"where $f(x)$ is the probability distribution function of $x$. We won't be using this equation yet, but we will be using it in the next chapter.\n",
"\n",
@ -826,7 +826,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"This curve is a [*probability density function*](https://en.wikipedia.org/wiki/Probability_density_function) or *pdf* for short. It shows the relative likelihood for the random variable to take on a value. We can tell from the chart student is somewhat more likely to have a height near 1.8 m than 1.7 m, and far more likely to have a height of 1.9 m vs 1.4 m. Put another way, many students will have a height near 1.8 m, and very few students will have a height of 1.4 m or 1.9 meaters. Finally, notice that the curve is centered over the mean of 1.8 m.\n",
"This curve is a [*probability density function*](https://en.wikipedia.org/wiki/Probability_density_function) or *pdf* for short. It shows the relative likelihood for the random variable to take on a value. We can tell from the chart student is somewhat more likely to have a height near 1.8 m than 1.7 m, and far more likely to have a height of 1.9 m vs 1.4 m. Put another way, many students will have a height near 1.8 m, and very few students will have a height of 1.4 m or 2.2 meters. Finally, notice that the curve is centered over the mean of 1.8 m.\n",
"\n",
"> I explain how to plot Gaussians, and much more, in the Notebook *Computing_and_Plotting_PDFs* in the \n",
"Supporting_Notebooks folder. You can read it online [here](https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb) [1].\n",

2
04-One-Dimensional-Kalman-Filters.ipynb
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@ -460,7 +460,7 @@
"\n",
"$$\\begin{aligned}\n",
"\\mathcal N(\\mu, \\sigma^2) &= \\| prior \\cdot likelihood \\|\\\\\n",
"&=\\mathcal{N}(\\bar\\mu, \\bar\\sigma^2)\\cdot \\mathcal{N}(\\mu_z, \\sigma_z^2) \\\\\n",
"&= \\| \\mathcal{N}(\\bar\\mu, \\bar\\sigma^2)\\cdot \\mathcal{N}(\\mu_z, \\sigma_z^2) \\|\\\\\n",
"&= \\mathcal N(\\frac{\\bar\\sigma^2 \\mu_z + \\sigma_z^2 \\bar\\mu}{\\bar\\sigma^2 + \\sigma_z^2},\\frac{\\bar\\sigma^2\\sigma_z^2}{\\bar\\sigma^2 + \\sigma_z^2})\n",
"\\end{aligned}$$\n",
"\n",