03. Discrete Probability Distributions.ipynb

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   "source": [
    "## Bernoulli and Binomial Distributions"
   ]
  },
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   "source": [
    "A Bernoulli Distribution is the probability distribution of a random variable which takes the value 1 with probability p and value 0 with probability 1 – p, i.e.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n"
   ]
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   "source": [
    "## Example\n",
    "\n",
    "**We want to know, out of a random sample of 10 people, what is the probability of 3 of these 10 people being left handed?**\n",
    "\n",
    "* let's assume that the prob of left handed people is 10% or 0.1 and probability of right handed people if 90% or 0.9.\n",
    "* we have to add up all the ways we can arrange the 3 people being picked.\n",
    "\n",
    "There are 10! ways to arrange 10 people and there are 3! ways to arrange the 3 people that are picked and 7! ways to arrange the 7 people that aren’t picked.\n",
    "\n",
    "This is given as:\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "120.0"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import factorial\n",
    "\n",
    "factorial(10) / (factorial(3) * factorial(7))"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05739562800000007"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# parameters are k, n and p\n",
    "from scipy.stats import binom\n",
    "\n",
    "binom.pmf(3, 10, 0.1)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### We can use this function to calculate what the probability of 3 or fewer people being left-handed from a selection of 10 people.\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9872048016000006"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum([binom.pmf(x, 10, 0.1) for x in range(4)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**we could plot our probability results for each value up to all 10 people being left-handed:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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 matplotlib.pyplot as plt\n",
    "\n",
    "plt.bar(range(11), [binom.pmf(x, 10, 0.1) for x in range(11)])\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('P(X=k)')\n",
    "plt.title('Binomial PMF')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see there is almost negligible chance of getting more than 6 left-handed people in a random group of 10 people"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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XBCjG5qIamAkSIAESIAESIIHjSoBi7LjWPMtNAiRAAiRAAiQwFwQoxuaiGpgJEiABEiABEiCB40qAYuy41jzLTQIkQAIkQAIkMBcEKMbmohqYCRIgARIgARIggeNKgGLsuNY8y00CJEACJEACJDAXBCjG5qIamAkSIAESIAESIIHjSoBi7LjWPMtNAiRAAiRAAiQwFwQoxuaiGpgJEiABEiABEiCB40qAYuy41jzLTQIkQAIkQAIkMBcEZiDGbFg3V7BgrKDzclzm4cMmqidNGIaJxfNN9HbH94JHI3TOGWhuBq8GzjabMM51MApc3MfJpOLZR9J8hARIgARIgARI4HgSmK4YcyxsnFuAebqMkk+MOY8bMM0qOi8cYM/B9p0qzFNNDJy4SqAYi6PCayRAAiRAAiRAAkeDwHTF2MsuGlf7GO0N0PSJscG6gZU7Qx/BIdrvJFm/KMZ8oHhIAiRAAiRAAiRwxAhMV4x5sLLFWOddE82n3gO+A1eMPbSwcX4RpmHAPFnFxlN7HCY0vTi8s4bSCQOGG7b1xBdWPPVqgI2LFSyaIswCKut9yBDheO5WYS63YO2Nk+IRCZAACZAACZAACUySQKoYe/78Od5++20pasRfcb6/f0ExJqcpl5sYuBrJftJESYie2MiVGDNPrKD5eARnz8HocRMVs4TWlvtASESNtgYY2mLO04G9tYEVYw3dV27Y1wM0l01UrvZVGMfG8PkwKsa2WiiJqdREX7bYzPIiCZAACZAACZAACRQikCrGtBATFibxX5zv719QjIk4hrerMk4Z91vCfywpZiXGyrf805qAdW0J5uU+pJtZSIwFYwpOc1o3lmBecp8LBgR0PFKwldDcjHViCz/FcxIgARIgARIgARLYN4FUMaZFmP/v/lIKijFnU1jCGujt2rBtG8OHDWmF6vpWW47TCYop77oWTuKC/1jYw1500bxQwoIrIkX+1WpMFVf9UYLIkvE00Vw1Qz5tXqo8IAESIAESIAESIIGJEkgVY9OxjI3QXTUQFkSDKwbC1i9V0oJizO6hZpqo3rIwsoXY20b73SJirI3u1RLM1Q6CtriJcmdkJEACJEACJEACJCAJpIqx6fiMKXHVeBKsASHGlm7EeY2p8GGhtv1xOX6aUli3jCYGXvRDdDwxBuSapsQQnVUTldDUqBclD0iABEiABEiABEhgQgRSxdiE0gAQnKa0bpRgnm1hMFL7jA2FQ77hc8gPJKzEmN+B395sJTvwv+pizSih+diG4zhqCtSbpgSQ14F/t4OqSb+xQFXwhARIgARIgARIYOIE3ogYA2xYt2uoyO0nTCyeraHt36oiUEx3mjK0tUVgu4qQz9jwQd2NW2xb0UbLZxmTUbtbWyifsgWULveiqymF79mjOkyx6vN1IEM8IQESIAESIAESIIGJEZiRGJtYfhkRCZAACZAACZAACRwpAhRjR6o6WRgSIAESIAESIIHDRoBi7LDVGPNLAiRAAiRAAiRwpAhQjB2p6mRhSIAESIAESIAEDhsBirHDVmPMLwmQAAmQAAmQwJEiQDF2pKqThSEBEiABEiABEjhsBCjGDluNMb8kQAIkQAIkQAJHigDF2JGqThaGBEiABEiABEjgsBGgGDtsNcb8kgAJkAAJkAAJHCkCFGNHqjpZGBIgARIgARIggcNGgGLssNUY80sCJEACJEACJHCkCFCMHanqZGFIgARIgARIgAQOGwGKscNWY8wvCZAACZAACZDAkSJAMXakqpOFIQESIAESIAESOGwEKMYOW40xvyRAAiRAAiRAAkeKwAzEmA3r5goWjBV0Xo7ZDR82UT1pwjBMLJ5vorc7vjedowGaoTxMJx3GSgIkQAIkQAIkQAL5CUxXjDkWNs4twDxdRsknhJzHDZhmFZ0XDrDnYPtOFeapJgZO/owXD0kxVpwZnyABEiABEiABEpg2gemKsZddNK72MdoLCqHBuoGVO0Nf2YZov2Oguem7NPHDYB4mHj0jJAESIAESIAESIIF9EJiuGPMyFBRCcWKs866J5lPvAd/BCJ1zBhr3+mieWYBxroORvDtEf72KRdOAYSygcqmD7de+x15b2LhQwoJhwDxZxcbTHho+65wvJA9JgARIgARIgARI4I0RSBVjz58/x9tvvw3DMORfcb6/f0ExJqcpl5sY2Co2+0kTpeUWrNjIlRgzlxvovXTgOGIu00H/konS5R6GQoC9HqJ3uQTzch9qpnMoBZy678B5NUDrrPBPC/qtxSbHiyRAAiRAAiRAAiQwQwKpYkwLMSHGtCDbX96CYkzEMbxdlXHKuN8S/mNJMSsxtnbfVW4i2MsOVswmBv5HnD7qRh19ocY2mzBPhcTdThsVijE/MR6TAAmQAAmQAAnMAYFUMaZFmP/v/vIcFGPOprCENdDbtWHbNoYPGyiZVXR9qy3H6SgxFvAn22yOhZwrFFUeleVrdHcFxiVtJdMxBfOgr/IvCZAACZAACZAACbxJAqlibDqWsRG6qwbqj4JLJwdXDJRv+Z36NZYEMfZ2CwNbiTkh6NR/FacUY1cCdjMAFGOaKP+SAAmQAAmQAAnMD4FUMTYdnzElrhpPghCEGFu6Eec1ZqF1KrTS8lUXa0YF7Z1gHN4Zpyk9FDwgARIgARIgARKYbwKpYmxyWQ9apawbJZhnWxiM1D5jw8dNVIwSWltxKYpnQ2IMDqyrJRjLDXRf2NJp37GH6D3ediMYon3GkA7+IgnnlYX2Kh344+jyGgmQAAmQAAmQwJsl8EbEGGDDul1D5YRYGGBi8WwN7ac+B/0AkzgxJgLY2L5bR0Xu4i+2ryhjzb93mW1h4/wiTHdri9aTLre2CHDlCQmQAAmQAAmQwDwQmJEYm4eiMg8kQAIkQAIkQAIkMH8EKMbmr06YIxIgARIgARIggWNEgGLsGFU2i0oCJEACJEACJDB/BCjG5q9OmCMSIAESIAESIIFjRIBi7BhVNotKAiRAAiRAAiQwfwQoxuavTpgjEiABEiABEiCBY0SAYuwYVTaLSgIkQAIkQAIkMH8EKMbmr06YIxIgARIgARIggWNEgGLsGFU2i0oCJEACJEACJDB/BCjG5q9OmCMSIAESIAESIIFjRIBi7BhVNotKAiRAAiRAAiQwfwQoxuavTpgjEiABEiABEiCBY0SAYuwYVTaLSgIkQAIkQAIkMH8EKMbmr06YIxIgARIgARIggWNEgGLsGFU2i0oCJEACJEACJDB/BKYuxpwXXTTPL8I0DBgnSli7acGePw7MEQmQAAmQAAmQAAm8EQJTF2ODmzW0N4dw9gBnt4fGsoHK7eEbKSwTJQESIAESIAESIIF5IzB1MRYusPOoDuOdNijHwmR4TgIkQAIkQAIkcBwJzFyMYbMJw2zCSqBtP91A9aQJw1hA5VIPgzsrMNYHbugBmsYKNh62sSbC6OuvLbQvVrAgpkLNRVSvDQJToc5WG7UzCzAMA+bJKlpPxhOlo7si/h6sm1Usmur5tdvbcBLyx8skQAIkQAIkQAIkMEkCqWLs+fPnePvtt6WIEX/F+UH/SfFzsRcQS16cLztYMUpoPBzB2XMwethA2fSJLggxZsJc3YD1yoEjFdMQ7TMmqrcs2A7gvLLQXjXHU6E7bVTMKtpbtozT3mqjalbQ3lGpyvyYC1gTz+8B9taGzMPGwYvqFYsHJEACJEACJEACJJBEIFWMaSEmLErivzg/2D8LrWUT9UfxdifrxhJMbe2SCTnoXzLGFjApxpbQ2vLlYrMJ81wHI98l7LRRdqdCB+smVu4G7mJ4q4zyLTVRKsXYha5PHI7QOWegei/4jD96HpMACZAACZAACZDApAikijEtwvx/D5KwdaMEc7WT4C+mRFDtwXgKUaSlphGD05Sdl+NcyPuuWPTn0zCaGEDFGbyuhKWe4gzGL1OUYiws4MYp8ogESIAESIAESIAEJkcgVYxN0jJmP2miZFbR2U3KvBJOYatZUCwpn7GIGLvYxci2YQf+C+ubK/DujUL3bDmlKXISjF9eoRhLqiJeJwESIAESIAESmDiBVDE2KZ8xZzNLiKlyiSnFpWtB135xTVuxYPdQM1bgF2PYamHJrKP/Op6NdW0J5qV+okM+xVg8N14lARIgARIgARKYDYFUMTaJLNiPGiidWEuxiPlS2WqhpB34HQfDsAO/dPAPiTGM0F1VTv2DXWENc2CPLPSfuj5fL7uomiaqNwcYCsHm2Bht9WG5tynGfPx5SAIkQAIkQAIkMHMCUxZjYlrR9dEK/W1uxpfVftLybW3RQe9j39YWsWIMwN4I/WtrKJ1QaS0sr6D52Od7NuqjdaGktr4wFlA610TfvU0xFl8PvEoCJEACJEACJDAbAlMWYwcvhFj5uHQjOHV58FgZAwmQAAmQAAmQAAnMB4E5E2MjWJtD2GI6cc/B8HETFd+eYPOBjLkgARIgARIgARIggckRmDMxNkTHm040sXi2js5z33Tj5MrNmEiABEiABEiABEhgLgjMmRibCybMBAmQAAmQAAmQAAnMjADF2MxQMyESIAESIAESIAESiBKgGIsy4RUSIAESIAESIAESmBkBirGZoWZCJEACJEACJEACJBAlQDEWZcIrJEACJEACJEACJDAzAhRjM0PNhEiABEiABEiABEggSoBiLMqEV0iABEiABEiABEhgZgQoxmaGmgmRAAmQAAmQAAmQQJQAxViUCa+QAAmQAAmQAAmQwMwIUIzNDDUTIgESIAESIAESIIEoAYqxKBNeIQESIAESIAESIIGZEaAYmxlqJkQCJEACJEACJEACUQIUY1EmvEICJEACJEACJEACMyNAMTYz1EyIBEiABEiABEiABKIEKMaiTHiFBEiABEiABEiABGZGgGJsZqiZEAmQAAmQAAmQAAlECVCMRZnwCgmQAAmQAAmQAAnMjADF2MxQMyESIAESIAESIAESiBKgGIsy4RUSIAESIAESIAESmBkBirGZoWZCJEACJEACJEACJBAlQDEWZcIrJEACJEACJEACJDAzAhRjM0PNhEiABEiABEiABEggSoBiLMqEV0iABEiABEiABEhgZgQoxmaGmgmRAAmQAAmQAAmQQJQAxViUCa+QAAmQAAmQAAmQwMwIUIzNDDUTIgESIAESIAESIIEoAYqxKBNeIQESIAESIAESIIGZEaAYmxlqJkQCJEACJEACJEACUQIUY1EmvEICJEACJEACJEACMyNAMTYz1EyIBEiABEiABEiABKIEEsTYCJ1zBmoP7OATLztYMUw0N4OX8bQJ81QLVuhy9qlKJxJf9oNvOMQATWMFnZfJ2RjdXYGxPkgOkPNOoXj2huj+tAzTaGKcsoPtu3VUThgwzEVUrw0QqtXMnFg3FmH+Ta/wc5kRFwnwqoc1cxGtrSIPHY+whdrIIUIyu3Jlv8+HCFtyVl9b2Di3ACOj70qOwH/HQuukibXwGOEPUuSY77dLa5Zt8YDj72YTxrkORr56Hj6oo2waBxr79hPH7PoKX2ExQn99DSUxthoGFpbX0HpSdHQdx5cgxgDrxhLMkJhwHtVloks3grJreGcFxqU+nHG8OY8O2BhkKrNsvLpY2WlOqnHkjudlD/XTJhZOl7HkE2P2gxrM5QZ6Lx04ryy0V02UQvWnSyX+DtYNrNz1v17+uzyeRwK520hC5uehzuPycNByJRQ35nL2+xzz0KG7JPr0pSt92MU76kNX1kORYWnc8P9wFrmeZVs84PgbFmN2DzVjBe0dB87ePmsgRxxvtq/wl8tC+2oP2yMH2HMwfNhAyaigveMPk/84UYzhSQPGO20MfXEN1k3U1psoB6476F8yUL23nwH8gI1B5m2WjVfDyE5zUgNJ7ng2N1C7uw17V1gv9QtuoXXKROOxr/fdaaNiNtD3XdKlEn/jGrr/Po/nj0DuNpKQ9Xmo87g8HLRcCcWNuZz9Psc8dMgu2ehd5A+tuaq0oybGtloBQ8C+WOeI4832FR56sQYAACAASURBVGmlUlpov8aMZDEmFWoVXU9jiYG9jPaO+OufohPnS4HpI2erjdoZYQ43YJ6sppjuXDH20MLG+UWYbviNp0FTX2J8sjErE6FIS/xPnPIUU3iXKlgUJlRjAaULG7C8ZOLysYb2iwTFon+9POmh7pZz4Uwd3d1xRQUHEhv9dZ22ARG2E4rbedFF80IJC6IcYjrxjpLBwXgcDNZLMC92A6bhcaoA/C+4FGb1kPAaov1OHCfFQHOUf13LaDAPauDauL+B6klTsqxc6mG4N0TvUkXmX9T5xlaQ3fBR0w0fLb/9VMcl2ksNPa/N+UsWHDBVnnqwblZVnZqLWLu9nWidHd4Zm5PztMnGvT6aom49M7wN66aOw8TiWX99D9A0Q++AtCL73xMAm02YXnz+svmOZf3V0PPaJjC8VYZhaoGtworya8t1JoudDtaW1fsYnKpOrnNfjuRhGj+Z/pWubOMLvimwtDofx5+ch8xyAciXhk7NxuBmDRXZbkU7bKIvObttK/A+N9F/pZ8DMsu/ntEWXw2wcVH3AQuorPe9af/E/k0kb4/7RlF3tQexL4fMqHiPdD2bJyuo39c/pUX5/P1kqF2Kpwu3O7fP1C4rrpVk8MB1iTCCZfQsPomMi7/fw/s+94ubFnopVn3VRjuRPsrZ0n3PAmQ/Nq5yYLeL+lk1LhknSli7aXl1BqjyR/qJ1xbaF1U/GHzX/BGrviDQ13rvzQzaopcVtw4D429o3EvsO9wyuP2Z5OtvY6FZNS/JlHE4O44p9hUp71n+PuYghikgWYxBDdqNJy7GnTbKrl+YtJBpX4FRF1XDN+BLy0sV7S0bzp4De6uNqplkulNwzRMraD4eyfCjx01UzNJY3GXGF3yJvUoPHIzQFdNzl3sYvgbwegTrVhXmsvZz0/lYk/nGng3r4xUYyxvYDsSjT0SaJszTNXS2bMjwd2somTX03A5cDSTac8vG8Ok2RmJ+QJgzH9Sx5Pex2+2gapZQu2thpPP3QnW6/njUlGMTAxEm6Z9fjIkOMmDFFA+lq/fsXx2i7AbMsy0MRFlf9dFcNlBaXkHt/lDW4fBONeBDKKa35VTprs+cq61zTh8Ns4TmYzEqOrB3tzH0CZFxMYP1LLmYC1i7ZcHeA+ytDawYJWw8Hz/hPxptDTCU8zOiTYqwa+j6BttxWLct6KldR4hKB9bVEszVNqxXDuDYyiTtq2/xTpRv6cFPWBhNLJ1aCvhdWteWAmHGafqPVPr1R1rMivMlGdfYX85G94IBHSaTxUsLg13xPkJOVW+cM7B2fww5rs79ORLHafxU+iU0HozgOI4UxKl1Ho48wSKbVa5iabg/ZM420Zcs/G1Nv89qOh/OCL1LSzDfH/tJZpc/pS2+HqC5bKJyta/aoGg/z4dqYE/t3xz0L5soCeEm6s4eYntnXG9+jM7TJkqmr9/d7aGxbPran2pXyb/ai7Y7Fd778Sv6GtNE+XIPYtbGEW4Tp0zUHur8ZjEu9n47m00sueWV/e+tNSyYyZY/2ZaMUqiPKqF8LtiPeX7SL7uyT248FH0a4IzCLh6q/J4LiOwnhmifMVEVfZJg4LqFVG6P+wV/nQV+OHs3sjjleRdT2qKXjjhwy3AiZdxL6zvC05Ti3JuVCSTknmSNw1qkBn94hmOK668O1lckv2e5+xjHhiU1QBXdFF/ycFn85yliDLCumtD+YUIIGFeUuBAZ9HzExHTmux1vOlMMQuEXXvyy9w9U4wyoxhC+JwYt87LyQcuOL/gSj+P2HQnTpx78vcvixdEDmsqHf4BSL4rfMug96M7r62f1dTVA6hdPNo6kXwfasiYrzZbTBxXfQK5jFH+9eIRgO1FFx2d984fzjsNiLMYSE9eY9fNx97w8yECCd9AKJJ4xLnTHvxplHjQ7wTa86EMJQikmpJhf81lgdU7Cf4P1LPPkT9PtWPJNl6v69gaSQFIxbUFaicM/KNQLrNuufCc81sJaXEP3QROm50sZtSAHkvWdiPdFW70g0j7VQu/uyvgdkvkZW8+SWHgDiy9ucRisz/1MTQf5xaefUueh/IjTxHYXU8eqXBntKpyG7APq6Mf+kIm2aWHFNPw/mALx5Sn/2HVD+t967SAQkRTtyf2lGLwMrGW6gLh9SGjQdx43YHo/xlSew2n5c1Os3QUZxPESdWpe1f7FCYzNprvwq8j7rcobLIsyHgSvjUsXaaOyj4r2Yzq/ss7cMciLRQhnz/Cgyh8YM+Is38KI4dWBF5M68PfV3q0EThNqi14y8iCmDDJP474lGD7UdxQVY5nj8AHF2L77iqT3TPDJ7sdk2zJMLJ5vopc1PoeB+s5TxZgcYFbFlJgaPL3OXQyg7rSJfIG9F05VbtD86prHY4WJCh8ZFL1KzhNf8CX2lc07lLBiOkPRWSixGZMP2ShjzPky1vg0ZTqxU3uA/WQDNW3yluZcHbeIS0z/etkNHKi8N9FcXkLjibaWBIIET/wvuOAY6QgmYRnTeVdJSzHmr98AO1E+tw2E/qqO04F1owLzRAX12wOMEh0/g8z9rFUuVB0mdcaBaWA3H5F2JyOKaQuxHN2O6aJrPfELJN0BO33U9fSiz7IcrLCYM9FpuZ2v98NHPO+KPXlNpxsjrvQvXo/F6210fat+/FPQIvU4IRTOVRq/aF1k1Xk49vg8ROP113GxNNR7lLTIKNi2ZO5Enft+5Rcrvz+f6lhbMYMlV/fS+ktnq4WKKabQ2hgkzlCK/Mf0IYGB1Z+nYC68s0LtTsXnvUNen+3FJtvVeEV5FuPg/ey6DwopkWpaO47EF+ijVJ7H/VhSnYk86nRD5dfvYaiPU3WbYOnx99UetiAHeXlibdFLxD2IlkEZIXz9e1rfEa7zUD4jqYkdBlLH4QOKMf8Y5P44V32gYJo2BgHx71n2c6KMkbYVLnjO81QxBmm1aGAAC03TV0FyClM0SvULZdzRqMqt3RvBtu3g/1gdEdMYRMa9Ss4TX0zjDRU+qSMWL99MxNjzDZSMEoTJW3HpoRHwEYjpSN0yqIruqGnW9UGiT5RXZP8LLo99U8gyUJLPmIohrkMLNrYo73En5uYi0NGJ8CW0NkPtwVbTZjrfzssB2mJbjhNrAd87fd/zOXFNwME8iVCqrXgCZPwgpHXJVNMHI9kut9F+N85vbhyPN8iIS6I9RkRtSIxhPHUo8qbbVXdV1a245lm7/HmLPRZWNPWcsAyrH0HiHVR1GbYWp7Ow0XvfVFOsI1UH27eC267E1XkgW0JopvCLpp+vzv1pxOUhGq+/joulIeOKGQhUHqJtWta5FmOFy+/Ppzoe95H+Uqt7mf2lM8LgttgyYAFr9+KmvET+Y/oQ+R5qK4c/T/48+I+LtDsVn/eeeH32OL5gv5DBODBbEDfA+fMfX964NqRzE2lLgT5KhRrnV6UVrTORboYYE/684bEvafmqzENYqGVwOlBb1DT031AdissBLhl9R7jOxbl+Z3QSvr9J76DgrmfgAu+d71n/YVw9R+o3MB4IptljkHBPCL5n+Z4bie08bmoLsD+nxY7TxZgWXXejplZhxl2521PO/D7TnJxiTOz0wplTjUFP9ei72x+XvWnK7PhiGq+OSP8V5uMc05RexyKeCzRKHZH+K9IMT1M66L1vIG6aUjYUbwpLxDHwiTElaDOnKV2/k2gHofPk/g284MqHIbKa0jO1h55N+HUZbOhR3uNOzJ8HLd7d6duEadhwDmR9e5ZW/91gusE8iXD+ztr/XNyvrSE6iWJMDEghoSaZxkxTXgr6iYk8Ld0YoH9pbNoWluOVuxZ6F8fXQrmLPVUibID2O5qjsGiKOET+9DX1aDoL1Vb9bVtuReP7FRnXuQUyFelkg/xEXzC2gIgni9W5eCIuD+nlKphG5jRlkGlgUMgof3o+3W2CEvrE7P7NVxOyDHpaz3fdbfu679F3hAW1yDSlqgch/vO0u9BAHh6Y3Todt4vg+yvzGOAavJ/OVKUdmCJMe//jrBcx/bu/HxPvn3aV0TwRmKaM6SdS25gXy/gg0Ffry0EO8qqfk/9Y3gy+i+ncdBr6b6gOxeUAl4y+I1znkbzpdNy/meNwXF8dimNmfYV4zwr2MdGsFrqSIcZEJ2li4cTCWLnq6AXY5RJK3py/e0M6Ppqo3hwoZ3nHxmirDyvWxK4ag9+B394UZnmfA39mfCqOFeEvsWfDjvUJCTsODtG/Wok48PsHrGCj1IXWf0Uj9TvwO9i+n+LAL1/SqlxB6QhHP7F4wLOMAcjpwC+cVoWTbqrfWOgFL7rPmHyZz7UxFE7xwlk90pFFOwt/JyYfCLzQgHQuFpbB+9tqj6PXwgG+rxZH2Bb6m0NVb6+30Vk1PUGraau/wXQLdTqvulgz1CIB4WCu9oMJCS4vsWgHFOfAr5w1xws25ONiKvHdFay4Fix5TdT9uRWshASws9VB61oX27EWY0BORYrnfBY5UZcirrAPSjoL1aFIJ3DhXC8du4ObMsbVuYdDHGTwi9S/WPIgHMqT6jwQuTqJy0N6uYqmkeXAnyLGMsqflU+kOfCn9m82rEfuwpM9B9tiYcyZ4HZDGmXEgX+rg1ohB34VU/52FxrIwwPzVMUYIPs1vWBB9qk5HPh9P0Di+vdAOw478O/20Tzr36Mxrp9Q44y5uoGBWKwkFiSNLPSfxg5+gpBchd0Qi5cc293/LdjPyVrxi5yDtkXdYOTfUB2Ka4G+O6PvCNe5P5+BdPRJ1jicT4xNvq9Ifs+y+zHhZrOClRtW9qyVxpDwN1OMScf9uF33hT+MmIf1+a54aYz6aOltGsQ2Euf0EnIvhHvgNobA0tqYrTAy4vMvT249DafhnouB3re1ReViO7q1hV6mLR4JNMpwnO4LE1imHdyuIthBO6EtGDbk5nj+HfylT4q7vYdYEl25pdZxBuMR2xxUYK6OF0yEc6by7Td9F9yBX+zS7eZj4ZoyvQbzEO0sAp1YAjv7eWe8TNxcRPmCWwa7j+Y5d0sPsRz+UgfbsYI6mG4wTyJRV5QnbFgrVrDKrxDIJfdttBItYyKdOKFmY3DNt7VFrLOm+rVsSD9LXTOiww2/J24nl7L5rpxaFatW/VZC2SZ9Jn03iUwWu/4tWJpoXwtOUyKmznXu9d80fpH6dx9KrHMdqf9vTB4yyyVscEntyh+3d+xubeHtmN1wtxAJti0ZPDSwpJU/Tz7hbm0ht64RfeLl8UpNJPZvYkuclfEO3zFb4nhFEyyetHxbW1TRfOif0kx/P7x4pO9jnnYXGsjDA/OUxZgQOuEvi3SvZKymLCLGhJR64euzTlRQu+3f2iKhn9gboe/1E2JXdrFTgF5R6lH2Drx2ZepFTDNoi17qoToU18PjXlrfEa7z0DvjJeM/SB2H84mxuP4qzzuY3Fekv2fJz4mCuVO5vpXX/uIWOc4UY0UiY1gSIIEcBOR2Bkkr+3I8zyAkQAIhAqFFZqG7PCWBeSdAMTbvNcT8HTkCwk8o7N9z5ArJApHANAnYQ1gvRmpqz9vjiT9wpomccU+XAMXYdPkydhIgARIggUkTEO4N3lZB4osqLfSTXLMmnTbjI4EpEKAYmwJURkkCJEACJEACJEACeQlQjOUlxXAkQAIkQAIkQAIkMAUCFGNTgMooSYAESIAESIAESCAvAYqxvKQYjgRIgARIgARIgASmQIBibApQGSUJkAAJkAAJkAAJ5CVAMZaXFMORAAmQAAmQAAmQwBQIUIxNASqjJAESIAESIAESIIG8BCjG8pJiOBIgARIgARIgARKYAgGKsSlAZZQkQAIkQAIkQAIkkJcAxVheUgxHAiRAAiRAAiRAAlMgQDE2BaiMkgRIgARIgARIgATyEqAYy0uK4UiABEiABEiABEhgCgQoxqYAlVGSAAmQAAmQAAmQQF4CFGN5STEcCZAACZAACZAACUyBAMXYFKAyShIgARIgARIgARLIS4BiLC8phiMBEiABEiABEiCBKRCgGJsCVEZJAiRAAiRAAiRAAnkJUIzlJcVwJEACJEACJEACJDAFAhRjU4DKKEmABEiABEiABEggLwGKsbykGI4ESIAESIAESIAEpkCAYmwKUBklCZAACZAACZAACeQlQDGWlxTDkQAJkAAJkAAJkMAUCFCMTQEqoyQBEiABEiABEiCBvAQoxvKSYjgSIAESIAESIAESmAIBirEpQGWUJEACJEACJEACJJCXAMVYXlIMRwIkQAIkQAIkQAJTIEAxNgWojJIESIAESGCSBL7CzuoHsH72b/ifSUbLuCZD4Kvf4dkPP8AX//pqMvEdw1goxo5hpbPIJHAcCDi7PTTPb8DyFdZ+1MTKuSbaN2soX9iA5fhu8nCuCTjf2Pju+7nO4vHN3PcOvrW/xf8eXwIHLjnF2IERMgISIIH5IjBE71oLzYtlGGZzLMbsHmrmAppPRW5H6JwzULq5PV9ZZ24iBL7/+jM8X7uOZz9q47++idzmhX0T+BZ/+tUv8fl7H+Dzn7Xxxc9+gxdXruPzX3+BIr9R/vJQxPEhrKt/AKtn35UBirH9s+OTJEACc0xgdHclKMaeNGAYVXRHKtODdQPGuQ7c0wmWxEb/chnlqwPYk4p1t4Pqch29acwCvd5Ge3URa3eHk8ptcjyFy/FnfFW/ji+7v8WzH1zHl18lR514Z5blS8zE9G8M71ZRutTL3+b++1M8r3+CnQ8/gLX6O4y+B/7fP/8C1g9/gz/lza6IY/V32PnVh7De+90U3qW8GTn84SjGDn8dsgQkQAIxBMJiTJ6HxZjfchYTR/FLDgbrJZTWJyjE3Ew4m02UTjUweF08V8lPDNFZXUD1zgyE2L7KsYfv7G8xund9n4P97MuXzHrad1TbW7oyyGfZ+v5bfPPdF/jyxx/g8+6uzNyffv4BrLVP8H/zZlXG8Ufs/OQDPPun/SjlvAkd/XAUY0e/jllCEjiWBN6EGBPWCXO5BWsvBrkzwuDmGhYSrHHDh02sna2idqmGyukqmg+jAknGf66D6J2Y9DIvqcHbvNjNtmi82kb3Shnm+iAm1iH661WUT5dRPr2IxTN1dF6kT3QVK8ef8dXfi8H+C3z3XRzYmCzJSwXKlxTFDK7bL7ponDbR3IxJ7LWF9sWKYru8iMXzLQxSraNCfJpYySuuv/4Un//gA7x4JtL+oxRmkvM3Dr6Hje3HffST/j8dKdH33yKO6/hy+1v69MVUYd5LFGN5STEcCZDAoSIQFmOY8jSl87SJklHBxosgptGDOsqnSygtL8I0DBjvRsXU6F4VprGCtjJQALsdrBgGVu6GJ1GH0tctt/UjmJXAmUzTrKOXMpdq3SyjvCzyvgBD5P1KWIw56F9SljUtv6QFz1hB52UgudBJgXJ883t8IQb7h5/g8yu/z72aMk/5Qpma4amFjXfKKAm2JwzJtvEknPwQ7TMlNB+PK0iK2FNNDDTs8CPiXLadJTSepAVSDzqDX8P64S8x/AuA//xETQX/yyf4vP4Z/l9c3DHXvvnsl7De+y2G9z7CF5+lKsWYp3lJE6AY0yT4lwRI4EgRiIixV12sGWbQgf+Gf63lAYrvWGguGyhdS4nvpRJYUTFmoXUq7L82QnfVgPGWbwGCzt5OGxUj32CrH4n8fdlF1TRRux8We5GQ6sJmM16MjbqoGpWxiJShh+i8a2RbZ/KW469f4MV7H+LZ37Yx/Dohf+HLRcsXfn6G59J30TAQEWNPmzCNBvoBY+AAjbiwofwOb1Vg5JjSHv3TdVh/96malrT/DV/8SHD+JXa+zBZyOknn+W/w7MfX8fnPPsNfuNpVYyn8l2KsMDI+QAIkMN8E1GrKxuoSDKOEtSstdJ6qwcXb2uJWHRWxtcWE/K/k4JdhZUKSGNtqYSnG6qQG6UW0tsK0HfQvmzBOtcYrRcNBUs+FNcuEcWYD24GBPuWhJDEmVqgaBpYudrCtWTp9NEwzKi4i0R+0HJEI3Qv7KF9SVDO4nijG3HZR8fsfSgG7go62oCblT9aBgaW0HwdJz/L6GyFAMfZGsDNREiCBI0PgdR9100Dl44xtMhLEmPOoHmt10oN07WGMlUIOygaq93Jatvyw5bMm6g/H01/+27HHSWIMNnoXTZV/s4Lm4wG67xdYSXqQcsRmFMB+ypcU1wyu63qOWMZgobWspjCN5Ro6m320zuZf9Tq8XQmsHp5BUZjEAQhQjB0AHh8lARIgATXorXlbZiQSSRBjapVn1B9LD9Lxztg2uhcSpjETMyBuaGtUM36RQdKziWIMwN4QnQuLSpAJC5/YgiO3RtxvOZIyus/yJUU3g+u6nqNiDIA9QPO0K8gMA4tiE2NtgczKm5yWN7B4NWXqPCsO3p8ZAYqxmaFmQiRAAkePgOvvdaGbvb/TRMUYYD+oSQFUfxRjOUsC7Q7QhaevUsTYUC5QqKF9v436addKJhz4s6bS3DzuqxyTLl9SfDO4nizGHFg3V7B4tonu/RZWXEf/PL5gKtvCaimEXB39Ak1kBkVmEjEEKMZioPASCZDAISAgncfHVgPDXET5nXL+/ye1cPDFISw7RhntnZzl3xRO1gbW7ueY8ksQY/uaphTZc/21jPd7+faVEt8dEBvhGksxfmgZ5U0SY1ut4ArSvRH6Vytq1WgegbrPciTldt/lS4pwBteTxJgQqabfD9HeRuf9khTgizl9wbTQjZ3qnkHZmER+AhRj+VkxJAmQwJwRGN4R4kKLqfzWGH8xHHuE7Ydt1M+7W0+I6aCcUzuDdSHockxRigQTxBhSHfjThJPtWj7W0M21o4D6BJRxquAUpch7ghizbizBeLcd2vfMdaA3GghvhOHnPj4uWo7xk8GjA5QvGNFMz+LFmMvkcj+UF7HdRfz2KKGA6lQL9rzCODYSXpwFAYqxWVBmGiRAAlMioDa59ARZ1h5MGblwdrruVFsNvUzfHHeK8p0NZLjuq1STxJhw1I7Z2kJ8OzNLOA1vlaUYzWX50ANzAUuahytNjL0VXdUpRXKBzWkLlcPLVOjgIOULRTXL01QxFiOiBlcMmJH93pJyPET7HfFjJU97ToqD12dBgGJsFpSZBgnEEHB2Bxjs5Jjeinl2ni7ZOwMMdt+gU8or8QFwMeCo/wfeEFU4pK+aKN/K2Od+p42yYSTsSh9TQ4liDIjf9NVENet7kXIvKgNG7M74wTzo6dDoRrLBcLFnCWIMcj8vAysfb4+nSne7qJ0qofmkQNsuUI7Y/ImlCe6q1H2VLynSGVyPF2OA2kR4KbDq1X7aQsWs5vbHE9m3rqrp+Ngd/mdQPiaRjwDFWD5ODEUCsQS+HXTw7CfXYf3wA1g/+ADW2evyXFx79qMPYL33S7z49z/jf0NPi13Ky6ebGETGqz9i52/dZ0V84v+PPsT2v4p5qD9iZ9W9Jq7/8EM8e1994DcU/URP7Z1t2AGt5cB+MRw7rL8eoLlcQnMzEGiieciKTO36PhZkuSxFaZEK4RS34arvGe2Pkzn4P91Qfmw+H7WFZeHbthHYJ0x+Dul0BWuXaqieXUPz/vaYsS/dwKH2mzsbnioMhJInckpRbHob99mdaHB5RX49QOwUr53HDROL4rNHP+2NP6E06mPjYgULJ0rqSwNn6+hsRRp2Qgru5QLlSIpoP+VLimv610fo/VS0gRIW9DS76/NYfzBeimo/76J5fhELJ90vIVxoof+y2HsmhL74oVK5nfHjYvqFZgopBCjGUuDwFgnkI/AnfPV3QiRdx47/W7nf23j50YdSUD3/F59Tj9yXqpTuRG3/Hs+lGAvF+ZfP8PwH1/HFv3w1o+/AuX44ehB2B2ZztYOhf8NQ6cid13cpH9ViodR3CLV1zCiwmq9YOuPQ8zH4W2hKq2DWNJTt+pdlfaZoXL7ZHuUtR1Ku9lG+1O9tJqVzCK9rq+N+pqcPYXEPa5Ypxg5rzTHf80Pgr3/AF1I4/Rovw58DedZR1q1/1N/UE6JhCealXobVw8buFWUFe3bXVXjf/wlf1T/A89/tRixt04OhxJhpqqmOhWVhsbFg+4WYTFw5bS9eGYynq6aXqYSYXedmbWko4LOUEGHKZd/gn3MLh5TIDnBLi+VS5JuYwUhdv7TcTvXBp6d/lrccSTnJX77s720mpXFIr+vp8bdz+jYe0mIe9mxTjB32GmT+3zyBL3+LZ0KM/f2nkY/ryo/oint/9ynEt3jhfh8xz95Qzr//Wgm5ym/w9fff4k8/v45nP/8PfBMWfDEEtm/X0Lw7wCgimmICp15Sg2TshpSh55zHDZhGNXvz09BzEz3d7aDq9x/LuQVA8Tyo7y8akW8HFo/poE8Ih25hEUyvI/VNw+jKx4OmPrnn85UjKb19lC/JDy4piUN73WUzt0L80IKdaMYpxiaKk5EdRwJ/+d1HUjQ9+9UXCOukP/3ctW6595SfUdaUkkvx+2d4IX3RPsTzK7+AVf8U/zecQCJwG8OHG1g7vYiVaz0MC7rwjKPNL8bg9FHPu+fWOIGJH8n9mbR17KAf1E7M3QBNmUbe7RsSIzrwDe0AHr9Tvxu9to682wltQ3Hg5CcWQa5yJKW2n/IdIzGm2ur+tn5JQs7rkyVAMTZZnozt2BEYTyd+8eTbYOm/+w9s/1g42v8SQ2kWE1N5Boy8WyEA+PpXyufM+nEHL78JRp/3bLTZRv3MIiqXu7B8rmv5nldirH7HQvd2C61rG+g89jnvByJxl9FH9kYKBJrBSch/7K0G+pnbVBTMlis8i9RlwRRyB9efU0p10HZXfhbZIDZ3BiYUMFc5ktLaT/mOjRjTU8AVtN/olHpS5fG6IEAxxnZAAgci8IVrvfoFvvp6HJHz9TN8WRcrIX+JnS9t12LmdooxeweNnwweffOvbTVV+YNf47/+GrxX9Mze6qJ5bhHln7YxyL0iS+XZXG3DeuXI7xC2zxmQDvyRDLh+VKnWl220zxfYJf+dKtovIgllX5ArPNX0nXTqMcXBTgAADyJJREFUP9cZr/7Lfjo7xH4sMdmx7iuEFjFG2t5Th0B45CpHEqH9lG8/zySlP9fXtRjLmsqe60Ic+cxRjB35KmYBp0rgPz9R/mJimwmxnYX+/w+/xpf//Ax/CQgod2orbdD0Zfb7rz/F8x9dx7P31FRnxPLmC1vk0N7pYeNvylg810Ivc58zB6Ong8A0p97SoXpvvARfp6+mmt781J3Mz04bFW+60kDqNJ4uQN6/FGN5SeUORzGWG1XBgBRjBYG9keAUY28EOxM9KgQ8B/3/828ITVLGFLGAGPvuGV68dx0v/sPGf3eVT5r1D59lrMCMSTLlkvN0A5W3DCzesFJCxdzSFoUYC99ciTEAw7tV9Z1EIcrMGnr79p0LcTjiYmy8RYjPuugTtkXvh+jFns6vGCtizU235BbllhU+FmTkIsVYBMkcXqAYm8NKYZYOCwEH//Whslp9/s9/zpHpnGIsvIWFt+fYL1zfsxxJpQRRlrEKSudb6L1IVydqF3ADpavWeMsKLcZipiPnTYwBeiAquCN8Cj9564iLsaziT+P+/IqxaZR2lnHqd4DTlLOkXjQtirGixBieBDwCf8SXwkE/vNmrdz984HaKMRalcci4LSxeYfiP7qrMe/v3wFU+YyVULrVzf75ITUmaKF8d7x+mPzuzFNk2Yho+YytoPx/TKXwkt7owUb0z4d3HKcYKV0XWAxRjWYT2e59ibL/kZvkcxdgsaTOto0Xg60/xudhD7Me/xdc5t5yQeyklbb74vY2vf/0RrJ9EP3HkDPx7jhXDqFZTlrCyLlZTFvuUCsTXApbr6OlVmHtDCAd+YznuU07uasp52enbdeIvrQ8mOr0r6evVlEl1WayKDhRafpTbyPCJ289qwwPlqvjDucqRFO1+yqctvDl9OJOSnv/rek88bm0xz3VFMTbPtcO8zSeBrz7B58JR/6yyVonvRwrHffX9yPQsx+4z9s0fsO3/vqUQeB/+wfNBG937aPztS3FPfP/yw3/D/6Qm5e4zdqaE6rUetrWYSn0m4earAVrnSyidLqN0chGVS534LTLmZJ8xVQr1se+FC6HPNiUUsfjlOdxn7G50QYVXrjmy5Hl5Ch14+4yllSP0jHdaoHy5vrfpRXwUDnRbnddPYR0FxgcvA8XYwRkyBhLIT0DuwG8gzw78+SONhhzeraF+e4BRQUNYNKb8V9QO/Gtvdgd+md0heu+X1PYbB/4CQVL5tbUh5wa+SdEAcL78HZ7/5CN8+Xx/lZVv53p3F/bCljwbg2tVlMSHzU8vwjTLWLtthSyNQ/TXqyiLD4ifXsTimTo6L4qXJV85kkDut3xJ8c3guu9HTvmkCfP0GtpPQz6cry20L1YU2+VFLJ5vYVD4hxV34J9BbR44CYqxAyNkBCRQhID6NuU8b75ZpDTjsOrblEtv9NuUIjfuhq+x06jj3B78yPWPm8AHyUf/dB3WDz/Czlf7UY7aH6g8hW9Tqra6+Ddd76Pww1sV+emlpXXtQyjqfUH65Gn55Ww2URJcXhahnLccSXHm/zZlUgwzve4M0Dy1iLV72pdRf1d1Cc1NTVJcK6H5eCzQ5OrgU00MdJA8mdZWwwKbTeeJlmEmS4BibLI8GRsJZBN41UPNXEJrKzvooQmx1ULJrE9u64h9FlwOVmYVnf2vc1Api8HybAuDFH1k3VjK8U3IfRYk92N6CqqBfkpegf2IRx23gbX7riDQflZGEwORx1EXVSO8s7uyGhbb102nlVWOJDD7KV9SXDO47nFcQ9e1dOlpWmNdkgWeNmFGvn2qrFzp3yEN5V+n9ca/jBHKF08DBCjGAjh4QgKzISCsB+XlBgaT/kzPbLIfTEU4yp8uo/lk/As+GGA2Z/ajBkpmFe3nB82Hsq6ZGY7delVpMdExYRZSDBnI8wHw4a1yYfE4fLSB1rUOLBepLrNxzv3Gpd1DzTCwdLGDbd2WnT4appnx4fIQhwLlCD3pne6nfN7DMz8Yon+zhdYdPeXrfirNvxBjq4Ulw0DFvwBFbmRczBF/dK8q633ltrbCzbywTDAHAYqxHJAYhASmQcDZHaCfsc/XNNKddJz2zgCDzJ38J51qMD41NTaBvcT2RuhdKcM0ltB8GkwjcrbbwYrYCHWfFgf7P36D5+9/hGdnP8L2v+bZpy6SA2BTWE8MRLcZiQn7pCEH5dRvWMY8Nr40REespDXLvqk0YZEyZbyGWUHz8QDd98tyK5RCkrhIOcYZCh4duHzB6GZ65rYl83TT9wPNQmvZUGyXa+hs9tE6u4i1u8VE1WBd1M8Rs8TPtHJmkxjF2Gw4MxUSIIFpEZjEXmKvhxjcbWLlhDv4nWoh+7sErp9SYad4AC8/wefviS1RdrHzkw9g/d2nkN+SL8hIW4NqD3M4EblWrML+ivYA7WsN1M4sYPFMA73dUFp7Q3QuLCrRIMSp2AolZWFnXBELlSMuAnFtv+VLim8G1+3NNlpXaqicWETlSg/DEFrYwurstknDwOL5DVjaApkrf+52M8bBF5rkSo6B9k2AYmzf6PggCZDAGyfwqo+GsB68tYL6egutawX+X1pD+Z0ySlqA+T73U7mVz/qgrA7Fpo0Es//u/gLbn73C9+63TT+/t+t+TL4IURvdC2KgzjvQaif5fX47VIiuVRPGiTW0faslhw/qKJ+uoX2/jfpp10pWaGFD0XIkMTpg+ZKincV1+YPCwMKF9ni6Fw6smytYPNtE937L90OhgHuDu3q7sACfRZmZRoAAxVgAB09IgAQODQHHQlNP4/iEVNb3/LLvF9iew51ei/toeh6OX//qQ1g/+AW++jpP6FCYfViC1C73i9lTsKGkvFPXj8kw6ugLK45YuGFUxis590boX62o74GmfmnCi3GiFq0Dl8+XrVkf6gUhxqW+/PSY2JPQ9C+KsbfReb8kLZCLka9fxOdW7WtoIJflND4KXp0RAYqxGYFmMiRAAkeRgDtVudpFwZk54K9/wPYPP4D1j5/BzvkFBz9B/amqQnvWuZaSxavZk7B4baEjLI13fN8l1dskGOo7h1JAvNtG0I6otjkxjHwWuH2Vww/Cf1ykfP7nZnzsbHWkFbezNZ6X9D4HJbnZ6F2M80d0t8CI+S5stAhuHGYd/UJTm9GYeGX6BCjGps+YKZAACRxhAsPbYu+tMto7xQrp/Lv6xNUXT76FI5z5u18ViMCd2ltuwUrd0iIcpYP+ZTGV6Fq2wrd953oVnuHfM0wvWjCU9VCKsbei/nXy00Z6xaUvzujhfssRjUldyV++pBimf32E7qrrB3au44l4/Tko44IQ9q6QirEuis1xs1b6yjK4wrSU04o2/XIzhTQCFGNpdHiPBEiABLIIiO93mgZyWZt8cf3p5+JzWm381zd/wld/X3CqUm5xYKJ2v7A9DpDPGsicWpX74S2ientbTpuJrFvX1DSZ+N6ntOm87KJqGlj5eBwGu13UTuVc2XqQcvhYBg7zli/w0GxP5BTkW2IbFtcytqdXTpa8larOU7F57hLqD8frUu2nLVRy7qMnfySYtTn4IsZs2R7W1CjGDmvNMd8kQAIhAl9hZ/UDWD/L+m5n6LFRH62LNbRut1A/U0O30M7xKi5lHRtv4BlKIfZUfgZJfGf0bz/C9r/s4n9jQ8VddKcBz2xgu5BVTMflWo/yrBgd9bFxsYLFkyWUlxewsLyG1uORJ85kjG6YhRMllE+XUDpbR2drLCB0qtG/By1HNEZ1pUD5kqKYwfXR4w3Uzi5icVksIllA6UIL/ZfjaUuRBft5F83zi1g4WUZ5uRQbJjar7g+Eysfbsbd5cf4IUIzNX50wRyRAAvsk4Hxj47si/lfSsrOAxhMHeL2N7s32Pr79JzKrLBu59vvaZ9m8x6TT/NiC4l0vciCtXr6d9Ys8O6mwkyhHUl7moXxJeZvBdetGCYb4JBh9xWZAezJJUIxNhiNjIQESeIMEvv/6Mzxfu45nPxLTfvkzovx0TJTONdG+uYaS2McpaJzIH5kUF1nfiMwfXXxI5cDtTRPGB8p1VU6V5d4WI1eUBQJNrhxJib7Z8iXlagbX5TTtAcX6DLLJJIIEKMaCPHhGAiRw6Aj8GV/Vr+PL7m/x7AfX8aX0g7ex/biPfsp/6yWgvgfoWsagNsgsH2BqR33IucA+UAVZiw91m6sd78PdBR8PBXc/qp7L0T706AFPJ1uOpMy8ufIl5Wj614XINeWH26efFlOYJAGKsUnSZFwkQAJvgMAevrO/xejedVjv/c5bnZYnI2pvp6rr5OxuGrqfbSq8xJQAWLriOrh71w9+ID/5JKae8rhj5U5ObeQ6y+9rTqccSQWeffmScjL966rtCavpRJvI9DPOFABQjLEZkAAJHAECf8ZXf/8Bnv3TF/juu/xe7WqPq6AYM9/vHXAwszFYL2Gigkzs0H66UfgzQ7kq1t1ZfyaCbJrlSCrsLMuXlIcZXBdW2fLlHkb5m/8McsUk8hKgGMtLiuFIgATml8A3v8cXYory4Sf4/Mrv8T/IM03pAHIvJtPdkV5s4LqAmm8rgfktMHNGAiRwlAhQjB2l2mRZSOC4EvjrF3jx3od49rdtDAt+Wkh9W3EN9YsrWLk2+enF41olLDcJkEB+AhRj+VkxJAmQAAmQAAmQAAlMnADF2MSRMkISIAESIAESIAESyE+AYiw/K4YkARIgARIgARIggYkToBibOFJGSAIkQAIkQAIkQAL5CVCM5WfFkCRAAiRAAiRAAiQwcQIUYxNHyghJgARIgARIgARIID8BirH8rBiSBEiABEiABEiABCZOgGJs4kgZIQmQAAmQAAmQAAnkJ0Axlp8VQ5IACZAACZAACZDAxAlQjE0cKSMkARIgARIgARIggfwEKMbys2JIEiABEiABEiABEpg4AYqxiSNlhCRAAiRAAiRAAiSQnwDFWH5WDEkCJEACJEACJEACEydAMTZxpIyQBEiABEiABEiABPIToBjLz4ohSYAESIAESIAESGDiBCjGJo6UEZIACZAACZAACZBAfgIUY/lZMSQJkAAJkAAJkAAJTJwAxdjEkTJCEiABEiABEiABEshPgGIsPyuGJAESIAESIAESIIGJE6AYmzhSRkgCJEACJEACJEAC+QlQjOVnxZAkQAIkQAIkQAIkMHECFGMTR8oISYAESIAESIAESCA/gf8PlyJOKSTgtksAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Roulette\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.31412504396776203"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = 18 / 38\n",
    "sum([binom.pmf(x, 10, p) for x in range(6, 11)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson Distribution"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Poisson distribution is a limiting version of the binomial distribution, where n becomes large and np approaches some value λ, which is the mean value.\n",
    "\n",
    "The Poisson distribution can be used for the number of events in other specified intervals such as distance, area or volume. Examples that may follow a Poisson include the number of phone calls received by a call center per hour and the number of decay events per second from a radioactive source.\n",
    "\n",
    "It is calculated as:\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The average number of goals in a World Cup football match is 2.5.**\n",
    "\n",
    "* We would like to know the probability of 4 goals in a match."
   ]
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