homework-w5.ipynb

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    "# BL40A2010 Introduction to IoT-Based Systems\n",
    "\n",
    "## Assignment 5, DD.MM.YYYY\n",
    "\n",
    "### Author:"
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    "**(1) Create two arrays with 10000 samples generated as [Binomial](https://en.wikipedia.org/wiki/Binomial_distribution) random variables via [Numpy](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.binomial.html) similar to what we have done with Poisson random variables in the tutorial considering the following paramenters of the Binomial function:**\n",
    "\n",
    "**(a) $n=100$ and $p=0.3$;**\n",
    "\n",
    "**(b) $n=10000$, and $p=0.6$**\n",
    "\n",
    "\n",
    "**Make the histogram (empirical) plots related to each vector and compare them with the analytical results with the probability distribution funtion given by:**\n",
    "\n",
    "**$$\\mathrm{Prob}\\left[X = k \\right] = \\binom{n}{k}p^k(1-p)^{n-k},$$ where $k$ is the number of *successes* in $n$ trials.**\n",
    "\n",
    "**Remember to use this [scipy.stats.binom](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.binom.html) in a similar way we did in the tutorial with Poisson.**"
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    "**(2) Read Section 2.3 and Chapter 3 from [Network Science](http://networksciencebook.com/) and generate three different kinds of Erdos-Renyi graphs with $N=15$ (fifteen nodes) using [NetworkX](https://networkx.github.io/documentation/stable/reference/generated/networkx.generators.random_graphs.erdos_renyi_graph.html?highlight=erdos#networkx.generators.random_graphs.erdos_renyi_graph). \n",
    "The networks shall be (a)  with probability $p=0.2$, (b) with probability $p=0.5$ and (c) with probability $p=0.8$. Discuss about the differences you see if these graphs represent communication networks.**"
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