Fix minor typos

02-Discrete-Bayes.ipynb

@@ -7032,7 +7032,7 @@
     "\n",
     "With that said, this filter it is not used often because it has several limitations. Getting around those limitations is the motivation behind the chapters in the rest of this book.\n",
     "\n",
-    "The first problem is scaling. Our dog tracking problem used only one variable, $pos$, to denote the dog's position. Most interesting problems will want to track several things in a large space. Realistically, at a minimum we would want to track our dogs $(x,y)$ coordinate, and probably his velocity $(\\dot{x},\\dot{y})$ as well. We have not covered the multidimensional case, but instead of an array we use a multidimensional grid to store the probabilities at each discrete location. Each `update()` and `predict()` step requires updating all values in the grid, so a simple four variable problem would require $O(n^4)$ running time *per time step*. Realistic filters can have 10 or more variables to track, leading to exorbitant computation requirements.\n",
+    "The first problem is scaling. Our dog tracking problem used only one variable, $pos$, to denote the dog's position. Most interesting problems will want to track several things in a large space. Realistically, at a minimum we would want to track our dog's $(x,y)$ coordinate, and probably his velocity $(\\dot{x},\\dot{y})$ as well. We have not covered the multidimensional case, but instead of an array we use a multidimensional grid to store the probabilities at each discrete location. Each `update()` and `predict()` step requires updating all values in the grid, so a simple four variable problem would require $O(n^4)$ running time *per time step*. Realistic filters can have 10 or more variables to track, leading to exorbitant computation requirements.\n",
     "\n",
     "The second problem is that the filter is discrete, but we live in a continuous world. The histogram requires that you model the output of your filter as a set of discrete points. A 100 meter hallway requires 10,000 positions to model the hallway to 1cm accuracy. So each update and predict operation would entail performing calculations for 10,000 different probabilities. It gets exponentially worse as we add dimensions. A 100x100 m$^2$ courtyard requires 100,000,000 bins to get 1cm accuracy.\n",
     "\n",
@@ -7064,7 +7064,7 @@
    "source": [
     "### Simulating the Train Behavior\n",
     "\n",
-    "We need to simulate an imperfect train. When we command it to move it will sometimes make a small mistake, and it's sensor will sometimes return the incorrect value."
+    "We need to simulate an imperfect train. When we command it to move it will sometimes make a small mistake, and its sensor will sometimes return the incorrect value."
    ]
   },
   {