Merge pull request rlabbe#243 from liorgolgher/patch-1

Update 12-Particle-Filters.ipynb

Author: rlabbe

12-Particle-Filters.ipynb

@@ -1277,7 +1277,7 @@
    "source": [
     "## Resampling Methods\n",
     "\n",
-    "The resampling algorithm effects the performance of the filter. For example, suppose we resampled particles by picking particles at random. This would lead us to choosing many particles with a very low weight, and the resulting set of particles would be a terrible representation of the problem's probability distribution. \n",
+    "The resampling algorithm affects the performance of the filter. For example, suppose we resampled particles by picking particles at random. This would lead us to choosing many particles with a very low weight, and the resulting set of particles would be a terrible representation of the problem's probability distribution. \n",
     "\n",
     "Research on the topic continues, but a handful of algorithms work well in practice across a wide variety of situations. We desire an algorithm that has several properties. It should preferentially select particles that have a higher probability. It should select a representative population of the higher probability particles to avoid sample impoverishment. It should include enough lower probability particles to give the filter a chance of detecting strongly nonlinear behavior. \n",
     "\n",
@@ -1340,9 +1340,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "To select a weight we generate a random number uniformly selected between 0 and 1 and use binary search to find its position inside the cumulative sum array. Large weights occupy more space than low weights, so they will be more likely to be selected. \n",
+    "To select a weight we generate a random number uniformly selected between 0 and 1 and use binary search to find its position inside the cumulative sum array. Large weights occupy more space than low weights, so they are more likely to be selected. \n",
     "\n",
-    "This is very easy to code using NumPy's [ufunc](http://docs.scipy.org/doc/numpy/reference/ufuncs.html) support. Ufuncs apply functions to every element of an array, returning an array of the results. `searchsorted` is NumPy's binary search algorithm. If you provide is with an array of search values it will return an array of answers; one answer for each search value. "
+    "This is very easy to code using NumPy's [ufunc](http://docs.scipy.org/doc/numpy/reference/ufuncs.html) support. Ufuncs apply functions to every element of an array, returning an array of the results. `searchsorted` is NumPy's binary search algorithm. If you provide it with an array of search values it will return an array of answers: a single answer for each search value. "
    ]
   },
   {