diff --git a/Exercise sheet 3/exercise_sheet_03.ipynb b/Exercise sheet 3/exercise_sheet_03.ipynb index 806e1c2..3495c43 100644 --- a/Exercise sheet 3/exercise_sheet_03.ipynb +++ b/Exercise sheet 3/exercise_sheet_03.ipynb @@ -272,7 +272,8 @@ "plt.ylabel(\"$p_X(k)$\")\n", "plt.xlabel(\"$k$\")\n", "plt.legend()\n", - "plt.show()" + "plt.show()\n", + "# TODO: The histogram overshoots the theoretical value every time." ] }, { @@ -337,7 +338,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "id": "bbf5c843", "metadata": { "deletable": false, @@ -353,10 +354,32 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "After trial and error, I found that 43402 trials were sufficient to arrive at an 1-sigma error of around 0.001,\n", + "with mean 0.486440 and standard deviation sigma 0.000998. Wolfram Alpha tells me it should be approximately I =\n", + "0.487595, so I am happy.\n", + " \n" + ] + } + ], "source": [ - "# YOUR CODE HERE\n", - "raise NotImplementedError()" + "def sample_X():\n", + " x = rng.random()\n", + " return np.sin(np.pi*x*(1 - x))\n", + "\n", + "n = 43402\n", + "sample_mean, sample_stdev = estimate_expectation(sample_X, n)\n", + "print(\"\"\"\n", + "After trial and error, I found that {} trials were sufficient to arrive at an 1-sigma error of around 0.001,\n", + "with mean {:.6f} and standard deviation sigma {:.6f}. Wolfram Alpha tells me it should be approximately I =\n", + "{}, so I am happy.\n", + " \"\"\".format(n, sample_mean, sample_stdev, 0.487595))\n", + "# TODO: Maybe I did not answer the question. Reading is difficult." ] }, {