diff --git a/04-One-Dimensional-Kalman-Filters.ipynb b/04-One-Dimensional-Kalman-Filters.ipynb
index 35a75c5..4086be2 100644
--- a/04-One-Dimensional-Kalman-Filters.ipynb
+++ b/04-One-Dimensional-Kalman-Filters.ipynb
@@ -454,7 +454,7 @@
     {
      "data": {
       "text/plain": [
-       "𝒩(μ=10.377, 𝜎²=0.037)"
+       "𝒩(μ=10.800, 𝜎²=0.008)"
       ]
      },
      "execution_count": 10,
@@ -472,7 +472,11 @@
     "    posterior = gaussian_multiply(likelihood, prior)\n",
     "    return posterior\n",
     "\n",
-    "update(pos, move)"
+    "# test the update function\n",
+    "predicted_pos = gaussian(10., .2**2)\n",
+    "measured_pos = gaussian(11., .1**2)\n",
+    "estimated_pos = update(predicted_pos, measured_pos)\n",
+    "estimated_pos"
    ]
   },
   {
@@ -722,7 +726,7 @@
     "x = gaussian(0., 20.**2)  # dog's position, N(0, 20**2)\n",
     "velocity = 1\n",
     "dt = 1. # time step in seconds\n",
-    "process_model = gaussian(velocity, process_var) \n",
+    "process_model = gaussian(velocity*dt, process_var) # displacement to add to x\n",
     "  \n",
     "# simulate dog and get measurements\n",
     "dog = DogSimulation(\n",
@@ -934,7 +938,7 @@
     "\n",
     "```python\n",
     "prior = predict(x, process_model)\n",
-    "likelihood = likelihood(z, sensor_var)\n",
+    "likelihood = gaussian(z, sensor_var)\n",
     "x = update(prior, likelihood)\n",
     "```\n",
     "\n",
@@ -1286,7 +1290,7 @@
     }
    ],
    "source": [
-    "book_plots.plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], xlims=(150, 180))"
+    "book_plots.plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], xlims=(150, 180))"
    ]
   },
   {