WIP - 21-11-15 L11.ipynb

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    "# Lecture 11 - 15 November 2021\n",
    "\n",
    "## INFORMATION THEORY\n",
    "\n",
    "In this lecture Information theory will be introduced following the so called Shannon's approach.\n",
    "\n",
    "### definition\n",
    "**Information** is a measure of uncertainty on a random variable\n",
    "\n",
    "### Example: Fair coin vs fake coin\n",
    "\n",
    "#### Fake coin (tail only)\n",
    "Assume to have a fake coin with head on both sides. The probability of obtaining tail or cross are\n",
    "\\begin{align*}\n",
    "\\mathcal{P}(\\text{tail}) &= 1\\\\\n",
    "\\mathcal{P}(\\text{head}) &= 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "In other words **Information of \\{\"Tossing the coin\"\\}=0** because I already know what the result will be.\n",
    "\n",
    "#### Fair coin\n",
    "In this case the probability of obtaining tail or cross are\n",
    "\\begin{align*}\n",
    "\\mathcal{P}(\\text{tail}) &= 1/2\\\\\n",
    "\\mathcal{P}(\\text{head}) &= 1/2\\\\\n",
    "\\end{align*}\n",
    "\n",
    "**Information of \\{\"Tossing the coin\"\\}>0** because tossing the coin is an unpredictable process.\n",
    "\n",
    "### Ensamble of events\n",
    "\n",
    "\n"
   ]
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