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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Data Science Principles and Practices (COMM054) Lab Week 4\n",
+    "\n",
+    "Please read this handout carefully, and attempt the tasks. You are advised to \"play\" with the given Python code to understand what it is doing. This set of exercises focuses on writing basic Python code to visualise data by Matplotlib. Do not worry if you do not complete them all in the timetabled lab session.\n",
+    "\n",
+    "This is not assessed but will help you gain practical experience for the module exam and coursework.\n",
+    "\n",
+    "You may need to download some of the csv data set files from the module SurreyLearn page and place them in the same folder as this notebook.\n",
+    "\n",
+    "For extra information about the functions provided by Matplotlib, you can search the API documentation here:\n",
+    "\n",
+    "https://matplotlib.org/api/index.html"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "You can import Matplotlib's Pyplot module and the Numpy library (as most of the data that we will be working with will be in the form of arrays)\n",
+    "\n",
+    "```python\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "```\n",
+    "\n",
+    "Use the code cell below to import the libraries."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Visualise Commonly Used Probability Distributions\n",
+    "\n",
+    "There are at least two ways to draw samples from probability distributions in Python. \n",
+    "\n",
+    "One way to generate random numbers or draw samples from multiple probability distributions in Python is to use NumPy’s random module.  \n",
+    "\n",
+    "Another way is to use Python’s SciPy package to generate random numbers from probability distributions. (We will see this next week.)\n",
+    "\n",
+    "Here we will draw random numbers from some most commonly used probability distributions using Numpy. These probability distributions will be visualised.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Among others, numpy provides a list of methods to draw random samples from distributions. \n",
+    "\n",
+    "* binomial(n, p[, size]):\tDraw samples from a binomial distribution.\n",
+    "\n",
+    "* exponential([scale, size]):\tDraw samples from an exponential distribution.\n",
+    "\n",
+    "* geometric(p[, size]):\tDraw samples from the geometric distribution.\n",
+    "\n",
+    "* normal([loc, scale, size]):\tDraw random samples from a normal (Gaussian) distribution.\n",
+    "\n",
+    "* poisson([lam, size]):\tDraw samples from a Poisson distribution.\n",
+    "\n",
+    "* standard_normal([size]):\tDraw samples from a standard Normal distribution (mean=0, stdev=1).\n",
+    "\n",
+    "* uniform([low, high, size]):\tDraw samples from a uniform distribution.\n",
+    "\n",
+    "More can be found at https://numpy.org/doc/stable/reference/random/generator.html#distributions"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As an example, you can visualise the normal distribution:\n",
+    "\n",
+    "```python\n",
+    "rng = np.random.default_rng()\n",
+    "x = rng.normal(5.0, 1.0, 100000) # mu=5.0, sigma=1.0, 100000 data points\n",
+    "plt.hist(x, 100)      # histogram with 100 bins\n",
+    "plt.show()\n",
+    "```\n",
+    "\n",
+    "You can try yourself. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "rng = np.random.default_rng()\n",
+    "x = rng.normal(5.0, 1.0, 100000) # mu=5.0, sigma=1.0, 100000 data points\n",
+    "plt.hist(x, 100)      # histogram with 100 bins\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For the generated random sample, compute its mean. Compare the result with the expectation of the normal distribution (mu = 5.0).\n",
+    "\n",
+    "You can use `np.mean(x)` "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4.993902151243572"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.mean(x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 1.1 \n",
+    "Visualise the binomial distribution for n=100, p=0.8, and compare the mean of the sample with the expectation. (You can vary the parameters.)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "rng = np.random.default_rng()\n",
+    "x = rng.binomial(6.0, 0.8, 10000000) # mu=5.0, sigma=1.0, 100000 data points\n",
+    "plt.hist(x, 100)      # histogram with 100 bins\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 1.2 \n",
+    "\n",
+    "Visualise two normal distributions: one with mu=1, sigma=0.5; the other with mu=4, sigma=3. \n",
+    "\n",
+    "To make it clear, you can first try\n",
+    "\n",
+    "```python\n",
+    "import numpy as np\n",
+    "import matplotlib\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "normal_1 = numpy.random.normal(1.0, 0.5, 100000)\n",
+    "plt.hist(normal_1, bins=100, histtype='step')\n",
+    "plt.show()\n",
+    "```\n",
+    "\n",
+    "Then try to plot two distributions on the same plot."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "normal_1 = np.random.normal(1.0, 0.5, 100000)\n",
+    "plt.hist(normal_1, bins=100, histtype='step')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "normal_1 = np.random.normal(4.0, 3.0, 100000)\n",
+    "plt.hist(normal_1, bins=100, histtype='step')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 1.3\n",
+    "\n",
+    "Visualise the Possion distribution. Choose the parameter yourself. Compare the mean of the sample with the expectation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "\n",
+    "lambda_param = 4.0\n",
+    "\n",
+    "\n",
+    "poisson_samples = np.random.poisson(lambda_param, 100000)\n",
+    "\n",
+    "\n",
+    "plt.hist(poisson_samples, bins=range(0, max(poisson_samples) + 2), histtype='step', density=True)\n",
+    "plt.title('Poisson Distribution (λ=4.0)')\n",
+    "plt.xlabel('Number of Events')\n",
+    "plt.ylabel('Probability')\n",
+    "plt.xticks(range(0, max(poisson_samples) + 1))\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 1.4\n",
+    "\n",
+    "Visualise the exponential distribution. Choose the parameter yourself. Compare the mean of the sample with the expectation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "\n",
+    "scale_param = 1.0  \n",
+    "\n",
+    "\n",
+    "exponential_samples = np.random.exponential(scale_param, 100000)\n",
+    "\n",
+    "# Create a histogram of the exponential samples\n",
+    "plt.hist(exponential_samples, bins=100, histtype='step', density=True)\n",
+    "plt.title('Exponential Distribution (mean=1.0)')\n",
+    "plt.xlabel('Value')\n",
+    "plt.ylabel('Probability Density')\n",
+    "plt.xlim(0, max(exponential_samples))\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 1.5\n",
+    "\n",
+    "Visualise the geometric distribution. Choose the parameter yourself. Compare the mean of the sample with the expectation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "p = 0.2  \n",
+    "\n",
+    "geometric_samples = np.random.geometric(p, 100000)\n",
+    "\n",
+    "\n",
+    "plt.hist(geometric_samples, bins=range(1, max(geometric_samples) + 2), histtype='step', density=True)\n",
+    "plt.title('Geometric Distribution (p=0.2)')\n",
+    "plt.xlabel('Number of Trials Until First Success')\n",
+    "plt.ylabel('Probability')\n",
+    "plt.xticks(range(1, max(geometric_samples) + 1))\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 1.6\n",
+    "\n",
+    "Visualise the uniform distribution. Choose the parameter yourself. Compare the mean of the sample with the expectation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "\n",
+    "low = 5.0      \n",
+    "high = 15.0   \n",
+    "size = 100000  \n",
+    "\n",
+    "\n",
+    "uniform_samples = np.random.uniform(low, high, size)\n",
+    "\n",
+    "\n",
+    "plt.hist(uniform_samples, bins=100, histtype='step', density=True)\n",
+    "plt.title(f'Uniform Distribution (low={low}, high={high})')\n",
+    "plt.xlabel('Value')\n",
+    "plt.ylabel('Probability Density')\n",
+    "plt.xlim(low, high)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 2.1\n",
+    "\n",
+    "We will test the central limit theorem by investigating the distribution of the sum of $n$ independent and identically distributed random variables. To do this, first we will need to be able to generate samples of a random variable $S_n=X_1+X_2+X_3+\\ldots+X_n$.\n",
+    "\n",
+    "Try this for uniform random variables, with $n=5$, using numpy to generate an array of samples from i.i.d uniform random variables, and then sum them.\n",
+    "\n",
+    "Set the range of the uniform distribution to $[0,1]$.\n",
+    "\n",
+    "Your code will look something like:\n",
+    "\n",
+    "```python\n",
+    "n = 5\n",
+    "s = np.sum(rng.uniform(...)) # sum n uniform random variables from the same distribution\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "# Parameters\n",
+    "n = 5  # Number of uniform random variables to sum\n",
+    "low = 0.0  # Lower bound of the uniform distribution\n",
+    "high = 10.0  # Upper bound of the uniform distribution\n",
+    "size = 100000  # Number of sums to generate\n",
+    "\n",
+    "# Generate sums of n uniform random variables\n",
+    "sums = np.sum(np.random.uniform(low, high, (size, n)), axis=1)\n",
+    "\n",
+    "# Create a histogram of the sums\n",
+    "plt.hist(sums, bins=100, histtype='step', density=True)\n",
+    "plt.title(f'Sum of {n} i.i.d. Uniform Random Variables (low={low}, high={high})')\n",
+    "plt.xlabel('Sum')\n",
+    "plt.ylabel('Probability Density')\n",
+    "plt.xlim(low * n, high * n)  # The range of sums\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 2.2\n",
+    "\n",
+    "To investigate the distribution of $S_n$, we can generate many random samples of $S_n$ and store them in an array, and then visualise this with matplotlib.\n",
+    "\n",
+    "We will do this using a for loop, although there are more efficient ways to do this in numpy (can you think of how you could do this without a for loop?)\n",
+    "\n",
+    "Fill out the code below to generate a list of $500$ samples of $S_n$.\n",
+    "\n",
+    "```python\n",
+    "samples = []\n",
+    "n_sample = 500\n",
+    "for i in range(n_sample):\n",
+    "    ...\n",
+    "    samples.append(s)\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "# Parameters\n",
+    "n = 5  # Number of uniform random variables to sum\n",
+    "low = 0.0  # Lower bound of the uniform distribution\n",
+    "high = 10.0  # Upper bound of the uniform distribution\n",
+    "n_sample = 500  # Number of samples to generate\n",
+    "\n",
+    "# Generate samples of Sn using a for loop\n",
+    "samples = []\n",
+    "for i in range(n_sample):\n",
+    "    s = np.sum(np.random.uniform(low, high, n))  # Sum n uniform random variables\n",
+    "    samples.append(s)\n",
+    "\n",
+    "# Create a histogram of the samples\n",
+    "plt.hist(samples, bins=100, histtype='step', density=True)\n",
+    "plt.title(f'Sum of {n} i.i.d. Uniform Random Variables (low={low}, high={high})')\n",
+    "plt.xlabel('Sum (S_n)')\n",
+    "plt.ylabel('Probability Density')\n",
+    "plt.xlim(low * n, high * n)  # The range of sums\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 2.3\n",
+    "\n",
+    "Try plotting your samples using matplotlib. You can do this using:\n",
+    "\n",
+    "```python\n",
+    "plt.hist(samples)\n",
+    "plt.show()\n",
+    "```\n",
+    "\n",
+    "From the lectures, applying the central limit theorem, we would expect:\n",
+    "\n",
+    "$$S_n\\sim N(n\\mu,n\\sigma^2)$$\n",
+    "\n",
+    "Based on the properties of the uniform distribution, does the distribution you have plotted appear to match what you would expect in theory in terms of the mean of the values?\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import scipy.stats as stats\n",
+    "\n",
+    "# Parameters\n",
+    "n = 5  # Number of uniform random variables to sum\n",
+    "low = 0.0  # Lower bound of the uniform distribution\n",
+    "high = 10.0  # Upper bound of the uniform distribution\n",
+    "n_sample = 500  # Number of samples to generate\n",
+    "\n",
+    "# Generate samples of Sn without a for loop\n",
+    "samples = np.sum(np.random.uniform(low, high, (n_sample, n)), axis=1)\n",
+    "\n",
+    "# Theoretical mean and variance\n",
+    "mu = (low + high) / 2\n",
+    "sigma_squared = (high - low)**2 / 12\n",
+    "theoretical_mean = n * mu\n",
+    "theoretical_variance = n * sigma_squared\n",
+    "\n",
+    "# Create a histogram of the samples\n",
+    "plt.hist(samples, bins=30, density=True, alpha=0.6, color='b', label='Sample Distribution')\n",
+    "\n",
+    "# Overlay the theoretical normal distribution\n",
+    "x = np.linspace(theoretical_mean - 4*np.sqrt(theoretical_variance), \n",
+    "                theoretical_mean + 4*np.sqrt(theoretical_variance), 100)\n",
+    "plt.plot(x, stats.norm.pdf(x, theoretical_mean, np.sqrt(theoretical_variance)), 'r-', label='Theoretical Normal Distribution')\n",
+    "\n",
+    "# Add titles and labels\n",
+    "plt.title(f'Sum of {n} i.i.d. Uniform Random Variables (low={low}, high={high})')\n",
+    "plt.xlabel('Sum (S_n)')\n",
+    "plt.ylabel('Probability Density')\n",
+    "plt.axvline(theoretical_mean, color='green', linestyle='dashed', linewidth=2, label='Theoretical Mean')\n",
+    "plt.legend()\n",
+    "plt.xlim(low * n, high * n)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 2.4\n",
+    "\n",
+    "Try this again, now with $n=10$. Does the distribution of $S_n$ look different, and does it match the theoretical answer?\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import scipy.stats as stats\n",
+    "\n",
+    "# Parameters\n",
+    "n = 10  # Number of uniform random variables to sum\n",
+    "low = 0.0  # Lower bound of the uniform distribution\n",
+    "high = 10.0  # Upper bound of the uniform distribution\n",
+    "n_sample = 500  # Number of samples to generate\n",
+    "\n",
+    "# Generate samples of Sn without a for loop\n",
+    "samples = np.sum(np.random.uniform(low, high, (n_sample, n)), axis=1)\n",
+    "\n",
+    "# Theoretical mean and variance\n",
+    "mu = (low + high) / 2\n",
+    "sigma_squared = (high - low) ** 2 / 12\n",
+    "theoretical_mean = n * mu\n",
+    "theoretical_variance = n * sigma_squared\n",
+    "\n",
+    "# Create a histogram of the samples\n",
+    "plt.hist(samples, bins=30, density=True, alpha=0.6, color='b', label='Sample Distribution')\n",
+    "\n",
+    "# Overlay the theoretical normal distribution\n",
+    "x = np.linspace(theoretical_mean - 4 * np.sqrt(theoretical_variance), \n",
+    "                theoretical_mean + 4 * np.sqrt(theoretical_variance), 100)\n",
+    "plt.plot(x, stats.norm.pdf(x, theoretical_mean, np.sqrt(theoretical_variance)), 'r-', label='Theoretical Normal Distribution')\n",
+    "\n",
+    "# Add titles and labels\n",
+    "plt.title(f'Sum of {n} i.i.d. Uniform Random Variables (low={low}, high={high})')\n",
+    "plt.xlabel('Sum (S_n)')\n",
+    "plt.ylabel('Probability Density')\n",
+    "plt.axvline(theoretical_mean, color='green', linestyle='dashed', linewidth=2, label='Theoretical Mean')\n",
+    "plt.legend()\n",
+    "plt.xlim(low * n, high * n)\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Task 2.5\n",
+    "\n",
+    "Now test the central limit theorem in terms of the average of $n$ i.i.d. uniform random variables. You can use a uniform distribution on $[0,1]$ again.\n",
+    "\n",
+    "The theoretical distribution is:\n",
+    "\n",
+    "$$\\overline{X}_n\\sim N(\\mu,\\sigma^2/n)$$\n",
+    "\n",
+    "Try this with different values of $n$ and see how the distribution changes. Does this match the theoretical distribution for large values of $n$?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 864x576 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import scipy.stats as stats\n",
+    "\n",
+    "# Parameters\n",
+    "n_values = [1, 5, 10, 30, 100 ,1000]  # Different sample sizes\n",
+    "n_sample = 1000  # Number of averages to generate\n",
+    "\n",
+    "# Theoretical mean and variance\n",
+    "mu = 0.5\n",
+    "sigma_squared = 1/12\n",
+    "\n",
+    "# Plotting for different values of n\n",
+    "plt.figure(figsize=(12, 8))\n",
+    "\n",
+    "for n in n_values:\n",
+    "    # Generate samples of the average\n",
+    "    averages = np.mean(np.random.uniform(0, 1, (n_sample, n)), axis=1)\n",
+    "\n",
+    "    # Theoretical variance for this n\n",
+    "    theoretical_variance = sigma_squared / n\n",
+    "\n",
+    "    # Create a histogram of the averages\n",
+    "    plt.hist(averages, bins=30, density=True, alpha=0.6, label=f'Sample Average (n={n})')\n",
+    "\n",
+    "    # Overlay the theoretical normal distribution\n",
+    "    x = np.linspace(mu - 4 * np.sqrt(theoretical_variance), mu + 4 * np.sqrt(theoretical_variance), 100)\n",
+    "    plt.plot(x, stats.norm.pdf(x, mu, np.sqrt(theoretical_variance)), 'r-', label='Theoretical Normal Distribution')\n",
+    "\n",
+    "# Add titles and labels\n",
+    "plt.title('Average of i.i.d. Uniform Random Variables on [0, 1]')\n",
+    "plt.xlabel('Average (\\overline{X}_n)')\n",
+    "plt.ylabel('Probability Density')\n",
+    "plt.axvline(mu, color='green', linestyle='dashed', linewidth=2, label='Theoretical Mean (0.5)')\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}