daviddoji/Kalman-and-Bayesian-Filters-in-Python
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Issue #332

Browse Source 
Fixed terrible wording claiming the sum of two Gausian pdfs is normal.
Of course, this is only true for independent normal random variables.
This commit is contained in:
Roger Labbe 2020-10-13 09:40:40 -07:00
parent 6abd93513b
commit 0efbce6012
1 changed files with 2 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
03-Gaussians.ipynb
View File

@ -1282,7 +1282,7 @@
"\n",
"The discrete Bayes filter works by multiplying and adding arbitrary probability distributions. The Kalman filter uses Gaussians instead of arbitrary distributions, but the rest of the algorithm remains the same. This means we will need to multiply and add Gaussians. \n",
"\n",
"A remarkable property of Gaussian distributions is that the sum of two independent Gaussians is another Gaussian! The product is not Gaussian, but proportional to a Gaussian. There we can say that the result of multipying two Gaussian distributions is a Gaussian function (recall function in this context means that the property that the values sum to one is not guaranteed).\n",
"A remarkable property of Gaussians is that the sum of two independent independent normal variables (https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables) is also normally distributed! The product is not Gaussian, but proportional to a Gaussian. There we can say that the result of multipying two Gaussian distributions is a Gaussian function (recall function in this context means that the property that the values sum to one is not guaranteed).\n",
"\n",
"Before we do the math, let's test this visually. "
]
@ -2140,7 +2140,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.6"
"version": "3.7.4"
},
"widgets": {
"application/vnd.jupyter.widget-state+json": {