fix broken cell

Code was broken before, this enables the cell to be run. Fixed some typos and added "None" to the  function "make_simple_step_size_update_policy()" for the argument "num_adaption_steps", which otherwise returned the error:

make_simple_step_size_update_policy() missing 1 required positional argument: 'num_adaptation_steps'.

As per documentation, None may not be the best choice.

Author: phosgene89

Chapter1_Introduction/Ch1_Introduction_TFP.ipynb

@@ -1208,7 +1208,7 @@
         "# Set the chain's start state.\n",
         "initial_chain_state = [\n",
         "    tf.cast(tf.reduce_mean(count_data), tf.float32) * tf.ones([], dtype=tf.float32, name=\"init_lambda1\"),\n",
-        "    tf.cast(tf.reduce_mean(count_data), tf.float32) * tf.ones([], dtype=tf.float32, name=\"init_lambda2\", tf.float32),\n",
+        "    tf.cast(tf.reduce_mean(count_data), tf.float32) * tf.ones([], dtype=tf.float32, name=\"init_lambda2\"),\n",
         "    0.5 * tf.ones([], dtype=tf.float32, name=\"init_tau\"),\n",
         "]\n",
         "\n",
@@ -1273,11 +1273,11 @@
         "            target_log_prob_fn=unnormalized_log_posterior,\n",
         "            num_leapfrog_steps=2,\n",
         "            step_size=step_size,\n",
-        "            step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n",
+        "            step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(None),\n",
         "            state_gradients_are_stopped=True),\n",
         "        bijector=unconstraining_bijectors))\n",
         "\n",
-        "tau_samples = tf.floor(posterior_tau * tf.cast(tf.size(count_data)), tf.float32)\n",
+        "tau_samples = tf.floor(posterior_tau * tf.cast(tf.size(count_data), tf.float32))\n",
         "\n",
         "# tau_samples, lambda_1_samples, lambda_2_samples contain\n",
         "# N samples from the corresponding posterior distribution\n",