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    "# Tutorial A13"
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   "source": [
    "__1__ Modify the coinflip section from lesson A13 to simulate throwing a dice. Throw the dice 100 times and save the outcomes $X_i$ with $i = 1, ... , N$ in a list. Plot the result as a histogram."
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    "__2__ Modify the code further to throw  $N = 10, 100, 1000$ dice and store the mean values $S_N = \\frac{1}{N}\\sum_{i=1}^N X_i =  \\langle X \\rangle$ in a list. For each $N$ repeat the experiment 5000 times and plot the resulting distributions of mean values."
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    "__3__ Repeat the experiment of task __2__ but instead of plotting the distribution of mean values $S_N$, plot the distribution of $\\sqrt{N}(S_N - \\mu)$,\n",
    "where $\\mu$ is the expectation value $\\mu = \\frac{1}{M}\\sum_k^M w_k X_k$, where $\\omega_k$ and $X_k$ are the weights and possible outcomes of the random variables, respectively. In the case of a dice the expectation value is $\\mu = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5$.\n",
    "What do you observe?"
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