diff options
Diffstat (limited to 'sem6/prob/stat1')
-rw-r--r-- | sem6/prob/stat1/Opgaver.ipynb | 150 |
1 files changed, 145 insertions, 5 deletions
diff --git a/sem6/prob/stat1/Opgaver.ipynb b/sem6/prob/stat1/Opgaver.ipynb index b398bfa..5967955 100644 --- a/sem6/prob/stat1/Opgaver.ipynb +++ b/sem6/prob/stat1/Opgaver.ipynb @@ -2,12 +2,12 @@ "cells": [ { "cell_type": "code", - "execution_count": 22, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", - "import scipy.stats\n", + "import scipy.stats as stats\n", "import matplotlib.pyplot as plt" ] }, @@ -91,7 +91,7 @@ "x = np.linspace(mean - 3*sigma, mean + 3 * sigma, 100)\n", "\n", "plt.hist(c, 20, density=True)\n", - "plt.plot(x, scipy.stats.norm.pdf(x, mean, sigma))\n" + "plt.plot(x, stats.norm.pdf(x, mean, sigma))\n" ] }, { @@ -134,6 +134,23 @@ ] }, { + "attachments": { + "ec517a6b-2120-43e2-98c8-d4325c259d03.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Opgave E\n", + "\n", + "As seen in the picture below $\\bar{x} \\pm s$ is $68\\%$ and $\\bar{x} \\pm 2s$ is $95%$.\n", + "Thus it makes sense that $\\bar{x} \\pm 1.5s$ is $85%$ as seen above.\n", + "\n", + "![image.png](attachment:ec517a6b-2120-43e2-98c8-d4325c259d03.png)" + ] + }, + { "cell_type": "raw", "metadata": {}, "source": [ @@ -142,10 +159,133 @@ ] }, { + "attachments": { + "952f465e-f534-46c6-a3e8-46ae5266ea6e.png": { + "image/png": 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" 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem 2\n", + "\n", + "![image.png](attachment:bf98f712-14a8-4e58-b702-d17957f3f0bf.png)\n", + "![image.png](attachment:952f465e-f534-46c6-a3e8-46ae5266ea6e.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 1\n", + "\n", + "No its not as $X$ cannot be described as\n", + "\n", + "$$\n", + "P_X(k) = \\left\\{\n", + " \\begin{array}{ll}\n", + " \\binom n k p^k (1 - p)^{n - k} & \\mathrm{for} \\: k = 1,2,\\dots,n \\\\\n", + " 0 & otherwise\n", + " \\end{array}\n", + " \\right.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 2\n", + "\n", + "Both $X_A$ and $X_B$ can be described as binomial distributions, as it describes the number of times a event happens given a probability and number of draws.\n", + "\n", + "$$\n", + "X_A \\sim binom(n=32, p = 0.5)\n", + "$$\n", + "\n", + "$$\n", + "X_B \\sim binom(n=28, p = 0.7)\n", + "$$\n", + "\n", + "## Part 3\n", + "\n", + "The variables $X_A$ and $X_B$ are independent, as they describe two different sets of matches.\n", + "\n", + "$X$ depends on both $X_A$ and $X_B$ and will change corrosponding to them.\n", + "\n", + "$X = X_A + X_B$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "There is a 0.11879701579425661 chance for there to be more than 40 wins.\n" + ] + } + ], + "source": [ + "# Part 4\n", + "\n", + "# There are many games here, so we can use the central limit theorem.\n", + "# First we can find the gaussian parameters for A and B\n", + "\n", + "mu_A = 32 * 0.5\n", + "sigma2_A = mu_A * (1 - 0.5)\n", + "mu_B = 28 * 0.7\n", + "sigma2_B = mu_B * (1 - 0.7)\n", + "\n", + "# We can then find the combined\n", + "mu = mu_A + mu_B\n", + "sigma2 = sigma2_A + sigma2_B\n", + "\n", + "# And then we find the normal version of 40\n", + "z = (40 - mu) / np.sqrt(sigma2)\n", + "\n", + "# Then we find the prob of it being under, and subtract that from 1.\n", + "p_over = 1 - stats.norm.cdf(z)\n", + "print(f\"There is a {p_over} chance for there to be more than 40 wins.\")" + ] + }, + { + "attachments": { + "ec5948a6-fd01-4ab0-8c02-1093eb72f7a3.png": { + "image/png": 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6LIv2y4l6D62J84DlTkwZfaEKz0KOI3XMj3pF+W/rcykIJp6EnMfv+r8ezkslVyLt8j6si+F5yGnE7a6vW5ZfgOVKnJoGIN9Snogcxn9V/HipcHBkL/gFGAcHLxUODl4qHBy8VDg4eKlwcPBS4eDgpcKROxBu94X39aHPwOrTMJobkcX3Klmhf89xZBcFuj1iFsTFTSjr3NqFYUFPJqlTg25bUsXrc+Z3WqJDtgYox/q37m7MuioLvZpdhlVto8ZaFAC0TPzlxav62REN9zbQaGKg12SWcG9FNZFI2dys+hN9y/RLZgUP1zTJFl5ne4cfrGmMU85p+rp26kT8pTp9sEDMGHcWiRmlNWIwMyU3PmPM/NHxpmAjdllWtY1uX+CBVr9vv6/Xo71A2zELf1+3bihKGiAaz1g31R3FJ8cQPRkFt86zoh0tSFk7FmgdKrDO76yQ7+0FicZSZ6RUmCTo48VS0U+qzpTMFo51hcrsKhWbw1YnF+Ckc/9b3FfQ+WH3VOffaEa1Xkxmzczoxxrd2tSoB2wWejW7TKsOjKq2KGAe4hElDxER0VnfQmeNRWK4t4F6EwM9MHKvwiRBl1xK6CdVZ0oezX4WZPfsUmRz2Oqks5pPp9VE1VkBatOPtjXAgXBW44CEcUNZC15L/N2gB95G7LKtOjCq2qKAeYh3/NkQAKKCUzZUNxaJZm+DOAY1hHoTAz0wUioOSdD1M5KzJHMjx7qdw6KTzt3kxWg30DiW+RK83FgzoTVqsc+Xn7MjPDW7KladNco4xBca1QOAxOA7y1sY1KbZ2+DJTfuxLDQxMFYqOUyCnic41rPBSc2foZxALZWZpSoEOq32Zkf3DjW7KladNMrK3v4hAJDS4cLMLob1Ge1tkLUmBrp/WCslQVdwjgMHrgOl67OZ3q/9ea/6Wye2xQ0WD4bAXS4TlKqXUKxLF1uGZQztlgMtJUv3UXqX+Fdc7AcVcPR4HH0N6CFEP34JwOvHYwDfN9L2IN29hRCajAieUn+/7NdB9oBNxl/PYneP/fs/bAjM946K5Q1PNuHY6RqsVknxJ62/1kvYeLVRB1p5qfy7rgBQpchu+WMjnSz0uuzarF5d6j3MG8D1pGpMo5pnjiXf7B4FAwDA/M5/o4YaP3nVehuoQquJgWPovamRkqDLOcfvEq2DR59tbKb3+WUO3R/vO5Y+/Ulykzy9Bo7JBSXqJRTr0sXWYSnjugUysnSpd6E4RhQ7ozTCiPYOdylDpIsQ/chguExM2NIR9ddS8hBU+NUSmsTJ3/Dn4EvmZb7/SdfJ+OtZ7O73QgdifOhKFcvmZYsCgxYtYt7cbjY9EDauDIlOajPp653RNb4WBl7vpbjZ1cVCr8+u1er1Eakh/YiIKgWzjcrAblGg1aPgI/Q0O/OQRKW3ARFRZHXWqFoTAz0w8ATMxuys4By/S7Sr3lUiJtP7mXzziKhqc4UuQVLG6m5VL6FYly6WDIsU6DaIZOky7yx82r8ILP11ypBeQvS2BVOIkgMHEBHVvymGZsvBb2iXSmT2ai9fJ+OvZ7G7h+IYqVtOy99XJfnz/CwS76USTXSfQj9iujDSp4lMUB8LvU67Vqv9kqhOXSKKEsKzM6pRKlLGfDXi9fFom2Zvu7YMdS8wFrJ7G2iUiloTg+x+AmaFu9dNAC3Sw6wDf6/8tzxgI8b0RGN3wFQ+HMB6cx0Adf69r7hqtBO0YWi5VwC8WGeufLFk2DO9qilwWxvFVSuAzOTODO9sfnnJ1T98uBQAerFCfP/hVsDDZ3068LBaKbC6Wb7iDpjKX5UPuqEbAAzyG54OeKKRO4Cqx/oAqApRVNXyhVQLFee1D0sWevkEEFYioP02ALhnoXde8bY7cCetJwbsttBT+0epHxxpgkfeHgMANVjv3QS794aVKhyyHwB2vVi6d7JoNTzQM/ZUE0h4NRVGNSA5bmpY/E2d9faPFN5fJwfrOmtqZfxi6NR9L9+Znr842YnS1Yk1Cs5xLPrhgoILR+Q+L4xUAJTfha3Knq9dSrEuWSxnXrf7QbRIlm7nnRw6CdHf9ArthJOt5+94A+vf0+u6cKoCFv56qLK7q1o+CUuplJs/65NP6gD1ak8S7iCspdKmBIAjlYujgPWmw++x1sFhs9Cz7RadXXLUO00BoEqdBUUlVgNGYJX5XQBhbk2YRtWgq0XBlg/LbvUBcFr+ZMEryKF6Zm+DA3sAAIn3vgcAuPSVzqs3MciZUlFwjo83X5nxmVxAZHEO+WZ9M5j/616ArcmeaFrKWC5ZLGde97dbJpKlMxnRmeo1CNF9QtYlFl4zYdeKNxC2RK/rEpTB2bpQZ3dXs3zSZDtd+k+Y2AVPPl9iOdCplgdnJQE8Od5PssaUX+vgsFno1ex+MPanbgDuT1zlKbXqC6x+sQGAsIZebKMq0NOi4HDXQjuKAcCUlQZPQ3ZvA5NwSrta/uaTPXF01MQgO0vlcEM7zvE2nWhM65dU5Ev33lSr0vwac3WrlzKWSxbLmdftL4dsZOmqNOzCmxC9hOjvrvy9X0KRLrMePyiej5UDB0iC5veL1CyfrGA7tb2GfbO15cixVjU+EmrS/RktJWseyC0ZJ/aX2PXr8evJl5A0ZqKnwmrcoeEm4FbEO2yjamC0KFBm78ob2FIBAPYp2G0fR8v/A5RTHgeV3gaNGwMAbmwZxXDIURMDLRi6V7Ewqis4x9tietkeySpLHj4+W/zm5xu9dKuXUqxLFjtilreRpbMZ0QkA4qGfEL1twIrdrdE7acOqd5g5cIDTNgZ25pmpYplOS/7jDCkwbsQ3tjOylKRUdqIZAOsL8/vys9Y4sb/U7hDMQfrob3yVVs9SQwBhaMU2qgK7FgX22bvb7v7aBgCAyW/JF6/oKcO7lxXK1XsbaMBRE4NsKhUbo7odH7nXiojhKotij3u1617NgHopxbpksUNmeStZOost3RvpAOKvQT8humu3fQs6omKTFWdqMnOgCpG/Xh0SyzJEPJSUSuGPjrQWX0NXiBf6bHw/E5kbSpQAog5YZiLlPOzGif2ldms3XXVv9IhiSquIRgUAu9wby4xqtCcA7FsUMLL36LXI+cJbztnhik+VD4/KcFjxzWGN3gYaUDYxcBCBs6ViI0GXcY4nIAGo+9r8uWAyvQellOs3cMT3uxSnoiApY3W3qpcwlksXy8jgw+29s5Kly7xLxH0AaOwaDmB57fgU/YTo75K7J9Dj72pSh8UcJFhcf2RWrJPw17PY3aMQAall+acNJKWS8sBjnrjXxHQCAE5+9RdWF84gZHxnvUQ/+rJMhz4WelW7Q1Pe6FNGaRWoiTvAkVWNPGVGGe0JAPUWBfac/GmdTn3XFwAudf+4s5H/8Jq9DdRh18RAJQKV0tcPKwm6lI+8aQGPF3vStkIeHrW2sJjeU4f7129U3w8lpG+eBO5yJau7Vb1IsS5bbB2WMrRLYSFLl3i30UKBTrS84qTQEQc7IHA06SZEr76NiGK8b4oOizm40qKQ1fVqsg6fEv56Frt7RItCHgFtV0iJ56X4Ip/41fWUgVFDcECcqzOJiCix1px5I9ODB60efNWaS9N1mQ6dLPRqdsMhmxSsEtGYl3//rr+tm6nFqF17AiLNFgV2nPwTkK9W7dq1q/gDbif1n4gOehuovVdhNDFgRpD1V5BE6RctnYUfnI4gouRMhysyWo5OJyK62b6EAfV09bqZtVgYVkOcdYPhnfnW2VSKiLgv1WNOorSz4RaNX9ipSxTOPHUnWZiMcxR/1dGbZ5llCYIb2jZTh0TSDbc3xLk59YS/l64T0TnxVd6MlkotGgfnWhzRuRuPNez+hkjpjNUq0e0D92fjjKpRTYjHTTt72Qn2K8isADnrcJiH5TXsXdP5p7vYGFI+zR49k3HB2aVxZA6YbPPn4xtE1AfiDzESfZk/+DKXX5dFl2V2qU8Z+f8Lweqx9yKIMqq1yjajOY+4N7JbYw7/tt4vPVLYuOFS+OkuNobfu2WPHuf565cELD+d1Nuyc6ftgBcBjDaJzT8KjWPevm4v3jlrHsvsAnuaymYtVr9YHg38evuX7DL6FOC/KdtV5nBxT6p7gohof/XFT3uxEcT2yRY1qZdex3d3nVvbs8ylD34WNk+19y2whIhiQrx9eh+0CqQ3/Nt+1YNaZ7Pos8Qu0aTuPvWGy76OJVjtt4Tor3L/ZpvRPIkcp/e+HBrrY44v+26Fp77YAIwQomsgK/z1V5Y+LD5a8yPpdoetdk+gu3fukkWfHdm93WFrMSRMyvfA/3PfbDOaJ8GZ8PMOIn6erhhZa+7+9K0+DaO8VDg48iw4ZR4HBy8VDg5eKhwcvFQ4OHipcHDwUuHIXcgmAvvwT3PGPbk3Siu5kmzfyMPiS1OT3X3ea7Swfu0sUcE7uThLJiXQZKJnTDrJ1J4VGOkvoMJgb5jAng2ZGnWSfidclHpj76wBX7PrvHAM/S/2V1Y/S5Ty5djCYVmignd2cZZMitBkomdNqjG162Tzd4b0/96yytD5/RgVBnvjBPZMyNSok/Q746LEG4azBnzNpvPCMfSXSriP8M2fLwVSLaeo4B3zyLO40rPKPi87C7WY6JmTakztOnn/9bcHkGKc3lJRYbB3hsCeAZkadZJ+p1wUvWE5a8TX7DgvdED/vcrm4gJR+bfCr1idooJ3zCPP4krPKvu8FJpM9MxJNaZ2nbz/+tsDSJFfp5wKg71TBPb2kKlRJ+l3ykXRG6azRnzNtn4H2tBfKqcSMwXHOlov3Yxbc8wjv92pVfqhyUTPmlRnatfJ+6+/PYATUGGwzyYCe5kadZJ+p1wUvWE7a8jXp/LtLP2lUjTW8guAV72cNeaYR54lkc0U+SZjk1lhas95qDDYZxOBvUyNOkm/DSlp+l0UvWE7mz0M/074qwr9PGAhU9/56X03AG9bS1lCBZ+4+Zxr5TcL2nPItxUVqPHIi9TtLK50dfZ5CWG+BfqZ6CWwus6cVGdqF9j8oUKnb2Pwr7w6Nm7Qi3KqfpvnSqp6GSJ33Kve3B+XIzMTJUtlUGOwF2nzcX2Z30BX7KtSBDBIYC9To0XSL+JzlxnKIY11Fm9UnFXxlX2CSc8La3KlHRPsTxU1fzWg/1Olcb+UD4p0mHrKNnDz0/rji9Q7AAD7X642Zbx/08MwH+zZ6ybS1vaclQzz5uARtyQKEsq+Btbi4YmTfmjXYIlSwsEqrH7t1QmjpgyRymbcX/Rj6G+tvk2vtgbITFjyw4WRDSaUrbn7978++nJjPQt3qIKayOY6a9KKwRt6TlIMmROWTYkFMDp84sj+Z76STy5o3fTLyBK7JxbcbxG73KfnCQKu9+hxnkTPMxOW/HDhs0bj/WrusjO5ekOPka6NN+HJwZCexwi41qPnBcV1Bj1KuRyUmWJ/CA/BykJ2pt7YYe9lXl1SRNhtsN/Iv1FRjbopGfLbXWdprhO8UXOW7Sv7BJOcF7bkZsTPnXVoY7OB3zFPFRV/NaH/CUDGOG8A6CA8m5FSwZ9220xEtNT7JoNDXgImj7yMup3Flc5mn5cyrIvQx0QvgdR1u0krmEztAjk+k9ReRv8vcOhLqPqlnst6AUgwGd8TEW3HDqKPBa962pPUqDHYWwnsiV7bkXpqWq8qCZZdJYG9Ntu8qIa0SPoF7Gx6gab+SBdf/keXi6I3as6qke3bn2DS80KaXGvHBOapouZvdjwBg8s3cbu+etllU9snwr5IBT/C73UA6OoygsEhz4a4mMFcr2OVCsO6PiZ6CaSuq4HN1C48AmCS2svo/4UnBRKqfqnnzF4AAICOANAuaEg6hrssApDu1s7eBRtzPvqZKr0zeOgQP+8oiFzgwIy27rUGe263UhMoCey12eZFNdAi6RdQu1bThcWKLnq5dh2Gi/Yc+6I3as6qke2zTjDxvJAl19IxgXmqqPmbHRdgADxe+W7/4Zpn5gt7Asl6GpC4q5EJADwqb87Am16hwMnW8TugyiEvW4yiMb/i8RU15nq1VXHHg+Lj4+Pjiyv5OS1M9OFnbPL2TPQiZK6rwMbUzpp8oVnfyqM2JMpJ7Rn0/xVfWZYMbOpu57kYEhRFDwAtr55F6fahj4A/WE8VbFx36ZuWXl7185wij9eXkp19lYBHw0a+aN1VEth7BclQxqReKhKS/pEPBJL+XVsk18b+P52/OnvGxXM/+TFcLDp76H0rx/7R3zxl3qg5q0a2zzrBbElUJLc+VE8VNX+zo1QsPIN1dxWyUO3a7jEvWJnpA1KuwCdkcyLWTCi/Aghrqa5NcoPqMrvdR/+l6/JEXHUBD9atW7duXfsfmIJlcBZQZ6IH03U2RKZ2lUK6O7VTpX9kYyEF10NJ//9h4lpgQyc7zzUJ9RGIs8Cgx6HAtmBWqViZ8/cOeh/ArO9CgwGRNh8Abn88Trw9Nul9XwOlGhlJf5GJwJPPlyju1fPlg4urScXFDzx/AoD7E1cVVXij5qyar6wTzEfltPDXOlXY/qpD/xOw2YuFk7nIa/8pZgpaObeTUVibQx6w55G3p25nMc0rx+wZ1mVwwESv4joLqkztFrBI7Vn0/zaqfgeeK85WBABtg+YOPFeddVBtzPknPgGwdMS8rsKZI3KBh0+eWVCUVxLYa7PNS9n3NUj6BSSOXz5xqCml6jvTPFguKjn2RW/UnFUl29c6wRTJ9VA/VdT8VYf+T5UnYZaNgIqKmcqelkvtiMAXNDjkASaPvIK6ncU0zxhzwIyvzUSv5joD6kztljOBRWrPov+3UfU74vSXF6qpLmAaeG7fb30YsyKD/eeFgA39Jg0Q9kTa/LOz5hYEblmpwJUE9tps81L2fQ2SfgHHjvw74N69AftPH2S7qODYF71Rc1aVbF/rBGMll51wFX+zpVQw2/Ks8khLxYTbyOOxABBx40uocsgDKjzyMup2lgRzlSozvh4mejXX7aHB1C6ASWrPpP+3UvU75PS36ACAhLD+xQD08fghw58hI2PO39X9s88tmzYC+0vTp7kD6UOtyVCw5jtgm7epgSZJv4BX/6uKmBhU3d+K7aKCY1/0Rs1Zi6+6mxSonhbshKv4mz2lEjYkDQBWxo8A5FTwo+sMzQTMHwUPBuw45CVg8sjLqNvtuNLVVskY1qXQxUQvQua6clKbqV0gx2eR2svo/y0c+iJVv9RzWS8AKQKXJQPmUaWmAoBf9009mB9pEub8wyG9Jlu3rQT28T083+g8Y3bDytZecQrWfAew8eBDk6RfMp6k4aKcY1/0Rs1Zi6+OmxTIzgt5csPtEu7IXy3ofq3Saf2il8at+3Ngs2tESir4tE87TB33ykQLo7SUQ17xHWEGj7yEup3sudLVVskZ1iXvI/Qw0cue+9tcZ0xqMLVbyPGZpPYSBn+RQ99G1S96ruwFIGL6muhhs2Z3GJYk7B6syzwkEgb7c35dM4mSLX5YCOz7naOUDsj/mZVcW8ma7wg2Hnxtkn4bHj7ScFHBsS96w3bWOuuoSYHyvLAlV9IxgXmqsP3VgP5S+Y8o5cji2f+p0N9HiAzqiUTE4JAnUmFCl1G3syTU+NPtmfH1MdGru24YLFJ7Nfr/OC3P7ZEoxnFsIVNCZLCPeCE4jYiW7RZ2LQT294jIfFo8HwwS2Et48DVJ+rUgrlNw7IvesJ0VfdXdpEAruXoSnm2lkieQBSb67EP2M/h/yGi1LmWwv13u5SdElNIqw3IuMWnzDRPYW9U4IOlXhWydgmNf9IbprOhrdjUpyDL+z35b7zwTfTYiWxn8t1S9hvMV7V8NSRnsE9oW2OwFxPYsa3npyabNN0xgb1HjiKRfDXKSfQXHvugN01nR1+xqUpANJ9f/EbLCRJ+dyE4G/58CryX3T7EflzLYv4XXevfu3tzLZLscZ9HmO0FgL6hxSNKvAqmLdhz7Em8Yzoqz2dSkIBvwf8VZnBUm+mxFNjL4p/+QnDaM8TtKBwz2DNp8Zwjsb3fYWkwHST8bmuuk3tg7K85mU5OCbACn9/4/RTYR2Nuz72cP5N4oreRKsn1eKhwcusAp8zg4eKlwcPBS4eDgpcLBwUuFg4OXCgfH/zdcDcr/dTiu9JiccEQnoXmO2XcCsfPj4saW5+fQcwKjnyolPBftzxFHPCsdXflQt31qXiMJzxoeFY+ueKA6mytc5Hh2pVLv65IGpJfc0i1UsGsfPdSzFvspxy8kGvJblycGUaDrBxqmDLvI8f9VKpr8J3Zg8dqrCrkbsG+YX16XJ4bhrmHKOQp8jv+jUjGC7caEDHzJxii//HY8NWx30kWO57hUdHHYZzPR/TM08tRNcTxNGHkCZg47mtnYRnBhYRe3Y3O3MctLOextVORK3nhVonsGeblon0FDn/jHmbSK7/szCdCZnoiwLpU4L4tKwWNvC9C6/K+42A8q4OjxOPpaNGVzUZTXJL7nyPXQ/9OW8CafRaZv+7psMBERrap0jhKbD6bYH6sgbOgl8zLXnUREtK/KccrYUuMQ0bHQt/BjaOhxiTCNmptJNEtiVCL0G/4cfMm8zPc/qXq2/aTpNXCMpOqOlP35CZ3vHEE3J5fKf3DaAZdREh0sT0TYlkqcl0V1/Gs3jLhO9KdfoXEPJQFa+MBjZ5RGGNHe4S5lJKasLkrklaniyFPQXyqJxQcTEZ1BMJGMcVzG5i5jlrdy2NuEWbzxTKJ7Bnm53L6Chv52wS+J6FD+j4lNgG7niahXslTqvCwqCY89izr/F6E9Zp0ysngECnyZvBrxPUcegP57lZG3xwBADYH0T8IuLmNzZzLL24SZvPEi2ITmTPsKGvpRjwYC8C1RD9oE6IwxyVKp87KoJDz2rAAtfHmKbmbCqExenfieI9dDf6n8WfgFcYWcXVxkc2cyy4vCTN54EWqE5vb2BYjqNgaVBFA5oicADQJ01pi4VOG8hKNe5LHXQ50vhVJejfieI9dD9219VLyUwPoCHqwDgPZ9ATlBvcgsX5UhvGXk6qkIWPEq24YPWz3DvgVWdTceyB7M+qvoYI1Jliqcl3LUf9htbS9sWKgSoAaU8j78lPu/L5UCsqOsRufOYJY/3FAizOKNF4Rkuwz1BVhnmVVdEGTNOFQI0GWeWFFIXKpBi2/jsdeizidGPI6p9jnyCHRfgBUqI31foEbnrmSWJ2CtRJjJG88gumeol9sXYFPnG3RNuKZJU9Wh8MQmJlmqQYtv47FXkSEAiGfE45Bqn+P/rlQwOuosACQ9BNTp3OXM8hYOe1GYxRvPIrpnqZfZFyCqG/1Q6DgxSEWHnScSvbalWrT4Vh57pow30gHEX2PEo6Hz3l8Z4MhD0P2sLDO4TRpRxhCP6mYiSm5a6wkRffYv0Y/4k4gyyhbJJKKkRt0yiDLbBGcS0VHMovSREuFjmE1EGY3OSPRahWi6RY9/pkw92/5MbCIS1Zk7lr1NRBP+IaLPsJ9I7qK9J6JeyVKp87KoiKgt1hIpA5yDnUREt1znEtGMBgWSpfEIvVtl8jKlLbE4lz4W5WDBSIfhr0MWzBl2MRCl55HILq5kc5eR4lt57a3CTN54JtE9g7xcYt+eht48ucHw6R/+qUqArvREAttSifP2HPU2HnsJdX7zwh6BrdOIaHnFSaEjDnZA4GibKRsFviivUDq50il+/uUhGOMBu17QH+cL+Fu+XBzuWprJHXjNpbR1MyO8vKtEmFI80y97llOsEoVkYKiX21eoi0op56KuQ+GJHJKlEufliPdnBWj15HZiRfdr8PdlxqOqkyMPgVPmcXDoAv9tPQcHLxUODl4qHBy8VDg4eKlwcPBS4eDgpcLBwcFLhYODlwoHBy8VDg5eKhwcvFQ4OHipcHDwUuHg4OClwsHBS4WDg5cKBwcvFQ4OXiocHLxUODh4qXBwcMBI164jd6R7bq/nwU7zOdNofmFY0JNJ7mq7uQX2h2HL4Rjv6U/D9PVlcXHzCuX5UjFAxBqy8FJc7MSQvjcSo7f3fJPyYKd57UbzTrr4zdwlntO3q+3qwtPIjeUwSFAoYEGkM54Y9tan3M7Vqcj70E2uV20tEdGveI+I6KJHPBEtwEk9K0sFE1GSV75bRrj8FkflBEPgYqHNFtuUUReJiOie+wo6P+yeyq6+GJ0ybBilghUD5zFTKaPHEye8HYe7eZ9dUv8FmM/bAOACFwCo3CvWz2in+RRDbdyPNs+JfwzuWqaMuggAOJ1WE1Vnqe3qi9Epw4bhrRwIQwvlkB5PnPA2///BZ4r+C7DMWjL20tr3hM8k/ZYMtnF/Bo3mneo0HwMPjd0cNJx17PGt6dRRejbe5p1SiZP/Jyl7L2f9ykON5k2au7kjRhZobzP+/NMAdF+ABYyS7bYxC+k22mle0rdeo9O8rJu9vV5Go3kjnebZjeZtLupoNG+TiP37P2wIzPeOZdyyGyw1YKfE4r0Bw5Kkibi7Iq5V20cFJKf+tr1mt35BsPdbPAxSnI9tERN6p0h/kbacdZSsuPbnvepvndgWN7jy6ti4QS8qMmw9RqoZQ+SOe9Wb+wOXIzMTJQvzEgze2/yG3tIdo53mJX3rtTrNSxrNM/SyGs3r7DSv0Wje1mnecaN5UeJe6ECMD11pu6kXdmUGlEqs3us3LEmaiG3lwjJXf++xXhz5ODSTwvwWk51JyWGQYg7mfBtJX5dLktyx2x0lK+aXOXR/vO9Y+vQnQUaeYdsxUsnYZMyc8TB5Y4WNRMe/dcMn14n+8PMb/zBP3dZnsVQMdpqX9K130Gne1v3dXq9Ko3ldneY1G80LneYdN5pnta63gmVApkTivU7DkqRJ7OTfSUSv4bRtJMptLBF95RapNCk/DCI64wsi2gfZSa04SlacyTePiKo2F72VZlh6jJgZm4zviYi2YwcRfSykqOf2PPYELItXqwY7zUv61jvfaV6l0byRTvPsRvPCsONG86zW9SxNVgMyJdK49RmWJM2Ge0PeaQ3A3U+8w3b3ugmgRXqY0qT8MEhuVepMgNjAUuIJw+B6cx0Adf69LwYnybD0GDEzBnQEgHZBQ9KB4S6LAKS7tctj9ypZLBWDneYlfeud7zSv2mg+WzrNO240b7R1vVyJPG49hiVJs2H0/T4AaF8L8SFC0Zhf8fjKDTxUmrQ/DACAc3Hv5wNwENWVnjAMFkYqAMov6fUkZlhxjOwzBsANANDy6lmgdPvQR8AfXfJYpRj4YgsTRjvN2/rWO99pXr3RfLZ0mnfcaN5o63qZEkXcugzbkmZDyppCLwM4ndBSosBl9paA1unWivDROgwAsAetAGBbzWLqR8mGkG/WN4P5v+4F2BmWHSONe/VAnK0DDNoYOhDbljxnpWKDzk7ztr71hfR0mj/ckKFXX6N5XZ3mnWs0b6AVvf1rJ0XcugzbkmYbuZLU3AVAGCSlcqtr/NYgHLezWEDl3A3zrwHgyplxUD9KtpHSvTfVqjS/xlxmhhnHXgWpCADQNmjuwHPV9T9UzyXIrifr+jrNi33rHXeaF7q/2+vV12jeUaf5LDSa19eKXmZAhDxuXYbFpNmQIVzl7JHcqmDowRVBQAaAzfLiLMN8fUN7m5sALEc3/JUMRwYfPj5b/ObnG72YGWYcexVcMdUFYBp4bt9vffJapWRbqejrNC/pW++g07y1+ztDr75G85qd5p1rNK9bQmFABkncOg1LkmZFRRdXAJHbJbcq+C+wHoArMGGbwqLdYQCAMwktAGBTjUq0wtOhwdjjXu26V1PJMOvYKxELAAlh/YsBQB+PHzL8/+9LJRJR4k4CEgFkRj8yA580eSsJwEjJ3Vr/4BHpQOYo8y0CEIc7QNR8AJmHQoB+HT+7A2BidwBxEP4tSXS0wElkFABLr2Tl6DpDMwHzR8GDAcRZvHksvB0t9+oi4b2lVCgR9wGgsWs4gOW141MgMSW4qKUTdgoRhQhpfiy7MgMyJRLv9RoWk2aFz4B9wPWeaS0lluvHRQOph8pEkpt8ufwwWGG5eLv+Cja+JRlWHCUrglLK9Rs44vtd6TYZaYalx4iZMQQuSwbMo0pNBQD4dd/UI89VirFXkBPaN/DyD2zQ5UMiImc6zUv71jvoNG9tNM/Qy2o0r6vTvGajeVuneS2dCoUU0aKQR0DbFdYJcVc0oFQi8V6fYWnSrEj+pO+Ib7+TvFUhiu1UffGCYdFLfEPOKUxKDoMoPqB4JhHRqPY/jRMH7Y+SBanD/es3qu+HEsdt3kozbDtGKhmbviZ62KzZHYZZ33YerJvH3qkQGe1b7wAOO80r+tZrdpqXdH+316un0bxmp/msNpp3KCEzABXvdRlWJE3Em/vjZIMPI33KASnujCsF+WEAgHuZwh3RhXyVHRvMbNPoO1cAUQNP3VLJMOPYy3E/LsgmcPzkB3nvQ4X3rc+zyPBvt/Ypmdob/FB4MRLzwrmq2aDvo2neeS/f/LuleRAnaqwGsPjxJ0/LoF96pLBxw6VwFlVtqXoN5yvmwUrhpZIXsfxifmDz6PlNnpbBGhPeOQkA//Vb8EIWVUUmmlJmDc6LWecXYHkQ4VP8KCH/iKCnaPJyaKyPOb7suxWyqij9h+S0YSWQB8FLhYNDF/gFGAcHLxUODl4qHBy8VDg4eKlwcPBS4eDgpcLBwcFLhYODlwoHBy8VDg5eKhwcvFQ4OHipcHDwUuHg4OClwsHBS4WDg5cKBwcvFQ4OXiocHLxUODh4qXBwcPBS4eDgpcLBwUuFg4OXCgcHLxUODl4qHBz/93DlKXjGeDT7aIngDgCSl+3ybtedJyS3gn+qPGMkdvQfVrjLKzG42tY0f777tzwjuRWcCf8ZY0zfIOBg21Ibey6tBGBlhfo8J7kT/FPlWR+AIACN11+p/l0lAOgaxlPCS4WDBaHHYtuhqTsAAK6pPCW8VDhYSAYARB3oPm0eABwrw1PCS4WDhXYLAJzutnDZm4MnZuLa9115SnIp+G39s8aaLS9cdp9WCuZfJz0oUWRJaZ4RXiocbNBNfx9hKy7Lra45eKlwcDxj8HsVDg5eKhwcvFQ4OHipcHDwUuHg4KXCYQh9TRrowfOTC8EfFj8b/B1MKL7FUxygjNTHiXeuHDmRArhFFucZ4qXCIWDUVOCjefbjadt+2Y4xE3iCeKlwCEhvegRY/xZr6t9+96M8eIZyG/i9yjOC2+qCwAc3WVPNj5RbyROU/SAH+7xULAj/1IlF60Md6FAIGEDZ+UBijwzWVOHNa7IclJZjTqUi+yJ/Rjj3uWJg+RZD613GPieVEt1lnrc+yS2hq/e0s2xXnZNUXVOHXMAQqt86iSjzK6wpb1cP/ywGJXFMGpCxVGghC5E/E8T3nqu4qq0117eUEQ30fCCt0b96RffPRifbTnLjM9o6pAIG8aQKkG93TgUlOiYLyFAqNJGFyJ8BMtsfJiKijHnd+r/dbgsREd2vEWFAw/NSKjP66Zc9j5niztamDnRIBIzitAdQ/F5OBSU6JgvIUCpIn4G8cAJ8Ivx9P5SI5mEyERGt78pLRYn4Qqf0C/+Mk5K9amsd6LAJGMdPAF4351RQNsdkARlKBekzkPuRWuISERFdLDKHiMwF3R4SEWWWOqZfxXNyWx9ao5Z+4T2+NSV7g352oMMmYByDQ4CtM3MqKJtjsoAMpQL6DOSBE6BCJQDAw7hQAKZi6RcBIN974/m9igJ1JmtMJqfKds0Bb0h3LyBCW4dNwAkklALcj+VEUBLH5AE5WmUAWYn8KaPldMvGvmgiSvNyTyQiolMeybpVPB9ErPEnf7Rt310R16rtowKS2c9dZkiFz8e2iAm9U6S/5RlUlSK7y0l10ILw7nVxYOfjBm/LBZxB4ZUtM9O6nyhgYInNf1tQVo8eNHnLlLb2rFu3GnLHZAGphqH179SBgdyP1ENjLVtNAWBH0ueFAADV6N+2/FNFis2mB9bNbeXCMld/77FeMvvZSJnwHMz5NpK+Lpdk2X+9l0zH/C17vK6MWHb/Ublv5ALOYRyAngbkRf9tQS3astvr8ohl9x+VmxD/QVjqXteTcsdkAamHoQ5HBnI/9uK+ZC8iyBZz3ZG6dTwfpTLPz7oVmn8nEb2G05b9nU0v0NQf6eLL/9iEO+MLItqHnZb9Pk1kOvrRBdS4QETvlpULCFK1Zah7wZFrmS0ALNUdicR/W1D9rR71CByWRGT2GC13TBaQehjqcGQgD5wA/uL29297f/rEuvNOF906no8LsHu+1o0h77QG4O5nuYRA7VpNJxczLRr1Th3bx+zeOhMAxNsW+0dJdVyoiBMYVgVAnFkuAAB4/1WZYReHXEX5VtSKx+BGFXUGIvHfGtTF8laPouI/8QSepJDMMXlA6mGowpGBvHAF7ituf4l7Q6uubiTs+F7UreM5K5XR9/sAoH0tTNaD/dNX03ebW517wSZ7Lu6rfAAOwvou2u+xVEeJD7DXvQcA89GmcgEAgFeQUd9KLOmIx+8f0ics9d8aVHGrR3SmdVkAB1FD5pg8IPUwACy8JzXWvJk+A3mhVApK94quqhR8VnhRX/Cebh3Px8PiVEtlpKwp9DKA0wktJRnIBxdXk7i/B60AYFvNYpYBU36pDl8/7GnoBeBIQju5gLPoMAxop09U5r81KJtH5x+0AIBt+drIHJMHpB4GAFcZrElxZCAPwCQ/z/P1eDDWErH+Ang+PlV8Hgh/ryQ1dwEQBlupJI5fPnGoKaXqO9OsXxAK868B4MqZcVaRB0VlOnArvAcA/J6vk1wAAPA4WmbYpZyOQ/HhnG5j9cUh89/mkNWjf9ESAK1rWkzmmDwg9TAA9FGxq20gDyDgoWVj44GvvQGUwz5LBP66dTwfpVLKcn5koBoA7LHdquDYkX+r/mD6rOmAg62EAdrbwgRgObrhr7aeAHC/qEwH9qAFAPOa5i9gZQ+JAABgxSL5v6/fqjh0LvGtxktM+uKQ+W9zyOIR9vrUA/Bv1JcIv1/P5pgiIPUwNKBpIC+gqDXq3okN3gLwBIV5qTBRIT7BDwAqurgCiNze3nZqvvoqEGNC1f3WgTMJLQBgU41KtOJNAEBkKZkO7HFvDGB/9JfYGScVAAB8+KFR39I7p2/Q+0Mumf82hywe0Z5mrgA2mTrjp5GiY4qA1MPQKhUtA8CFnb18c/cJUDbuoXC3UrFCGwA4JdQ+ENFat47n416liekEAMBnwD7ges+0lrLZlCTJjuXi7Por2Gj5ieLRl2U6EFbfE8AdvIIVfaQCTuKjk1sC9MrK/Lc5ZPHoXOwrAHC9WsA9UwnRMUVA6mFoQNMA0OPjObn9BPA8JWwMeuwB4PbaCl8BAMxnWvJSkcH/pWPCxvQG/T5dGgx5fiZNkexcKF4DAAaG/3xaaGF6LaG1TEdK5BsA0C7on+EfFpAKOIfJy9dV1i8t9d8WlMWjcy4dAKBvaug3EyWeKwJSDUMD2gaATqVa5PITIH8LS67eb//28iNL2zT7R/iQuZDWWL+S5+IVJM2pJ9np6KfxZd6Y28Lf8xctAzNaKnScTScioieHEhQCzuB30yLDa6z+24ISPEq5LuxFH82QOqYMSC0MLWgayBNY0Ni6lbx55jLbD22+fle/iuekVBJ9j9u20wt2MbDSXH4dQwdTwAkc9hxteI3NfxWHHDjmYJVTqcn9SC17kRVB2dP6VTwnX8IvNO5nACdqrAaw+PEnBlZuL95ZpkNDwDhudHx9InMik/mbe4X/Kg45cMzBKqdSk/vhPn4mY3RdjZoGdDwfnyqU3vBvok9c/iDaVHihgXUPap2V69ASMIoH1RoksWc+vsQaVfrPdMihY5qrnExN7kdmm332EdS/a0DDc8MDdrvD1mLhU/woIf8II9896d65i1yHpoAxZLxx6XAx5szpj8NYw3b+sxxy7JjWKmdTk/vxcMAiH8XQ4PcbGtHwnHyqEIUPd2LRmlUOdCgEDOGjgir/lk8ELMpyUFqOOZWK7Iz8meCu8rZwrbHfO3N2yWeGGSO3ML/6lTr9e7pb4HnLRu7H8/G2Pjdi42c/Myol89TaFdHoxSsl94F/qjwjnGgeOFA2kJGSknjn5qUUAAjL7a/0eKlwPC1EN7itPlku3PT8ZCLPgF+APRscfEVjMphXSi4E/1Th4NAF3jSCg4OXCgcHLxUODl4qHBy8VDg4eKlwcPBS4eDg4K8gnxp2b6/fZcfpO807nf/rQfX3HEk/mn20RHAHAMnLdnm3687Tx0vluUHSnjFFT9X7PKb4vJQR7oGF38Cnkm+2DG+gkE58q9uw3V2arCp2te978703fzuOJ5CXyvOCv968kRbUCb50bjbgdQcY/kSctCMB/3FREF5p37bVxveWVgLeSjlan2eQl8pzgje95rzQFziKL4DbN+oDJeXz/4q95KsuRb4gAI3Xv159UyUA6DqDlwovlecFXghrDmBP1ReAjQE17Oabi1z4+QA3AEDboTN3vAoArqk8gbxUnhvQ3vEA9jYDsLKry5pu3a7YpkwzWgAuUuFkAEDUge7TggYCOFaG54+XynODc/GvAKkHBwDJB76KvYQ1WsLtFgwATg9cWCV5cOIol2vfr+H546Xy3OBUhcrAZZdWgGfTo3u+0hZuGfP+C5fd15TCH79OmlaiyBJ3nr9nDv57laeF9DRvgB76AkCsY0Jvuulv4eKJcynMs8dLhYMjr4B/sYWDg5cKBwcvFQ4OXiocHLxUODh4qXBw8FLh4ODgpcLBwUuFg4OXCgcHLxUODl4qHBy8VDg4eKlwcHDwUuHg4KXCwcFLhYODlwoHBy8VDg5eKhwcvFQ4ODh4qXBw8FLh4OClwsHBS4WDg5cKBwcvFQ4OXiocHBy8VDg4eKlwcPBS4eDgpcLBwUuFg4OXCgcHLxUODg5eKhwcvFQ4OHipcHA8C7jqllxJSH6Cqq9i111kJqJgH4OWbOtxdjegd33Mgri4CWXV52Pnx8WNLe9U6AvDgp5Mcje6yrDB68vi4uYV0juThXiMO8BhBPo/VfyTPui/sUggUMh9Qq9phcsD1LxGkn5LAenD+68s+QIAn5SfPo0I1LfKs9LRlQ815j0qHl3xwKnIv5m7xHP6dsPLDBv0KbdzdaqOGSGbFvXGUuusA1AY59BOkn68ifXCxjR8RESU5JXvlr3U4ii19W/hd8vWvs6OrVn1LMBJbTkcIydwz30FnR92z4HfrEHDBsfhro4ZazYX45gkterZdDSp7gBjGftQckhh5F7FBBdhI79w3eZ56lQJe6mjqv/BzHCzbJXX8Zli1ePoEsnduX8Rp9NqouqsAAd+swYNG8yva8aaTXdZao+m6kiRQQcYy9iHkkOKLN3WV6jBGNRzTWMyOZYR9VBOBB4DDx1+b8fTgyyb1p3t+lJkCNv1HkqObCsVFpZdz116NOrVsb2cdyIrWXDSu2ceVB6Fq/NLU1fHxg16EYkb4mJH+q4KL9K2CnB9xURsCESVOsCjk80dafhnl3+hCv+NAYDrf8VlNnvdNiPRA1Dq75f9OlgeCykEbaBte81u/YKA45cAvH48BvB9I20P0t3bikKJm8+5Vn6zIBD793/YEJjvHZY9m5Bk0KZdiTtb4+K+frDzUs1WxYE7W+ISp4T/UbiHt0QLACByx73qzf3ljspnLNmUpdbqgHdkZiKalsbpu+akdj5aLoMRq9wBZlCCPdmR5FAiC58q5oRlU2KBzIQlP1z4rNF4v5q7gISyr1mnO7dY7kDB6PCJI/uf+QoAVr/26oRRU4bYpiR6gJuf1h9fpN4BsARtGJ446Yd2DZYA5oM9e91E2tqes5Jh3hw84pYos//lalPG+zc9LOxJH/lI7IlCkkGbdiUy7i/6MfS3Vt+mV1sDZMTPnXVoY7OB3ylNrd7QY6Rr400MVbYZSzZlqbU68ORgSM9jBFzr0fMCabqsFqvoADMowZ7sSHLY/zfWjxDUbNOmTZs2bSphCBERLRKeBc1DSCqR2et1IqKxCBekvww4bLd+g2Xr7hAielwwk4ioDhEdMO0iohumLaKwTc9vaJdKZPZqT2zBUBwjoii3sUT0lVskEbUtmEKUHDiAiKj+TVHytNtmIqKl3jdty+ztyYSsg1LtypXfYQwR0UxsIqJv3YaZ7wT/I9cyGd8TEW3HDqUq2Ywlm4J6y47VgY+F3Z7bHbrMilVmhh2UYE92JDmcfwIGjP/nn3/++eefoZZdy42xJxq7A6by4TLZ72MaaBQogIcPlwJALwBDy70C4MU6c5nCr7gDpvJXoSXo7nUTQIv0MADvP9wKePisTwceVislyozwex0AurqM0AiRKSTVroQbugHAIL/h6YBnelVT4LY2Si0dAaBd0JB0O1WSGdljBsUzh+EuiwCku7XT67K6A+ygPDSOJAeA7LqtrwYABdPkgxpPucgM4IVmfSuP2pA4DIg7HhQfHx8fX/yyA+3qgkVjfsXjKzfwEMCbXqHAydbxO4D174kiibsamQDAo/LmDFXP2EJS7fZwBwC3duFnAKA+S4vwkLzl1bN2qiQzWijdPvQR8EcXvS5rOKAdFPNIcgBZuq2XwEeXlK/t9uCxJwBsGbl6KgJWvIoLeLAOANr3daBdQ9Bl9paA1unIB8AnZF1i4TUTdq14A2GS24sLEO6rEZBypaqajypCEu1qKIOzdQFhOVtLIM7WYasSZrQwaGPoQGxbotdlLQc0g9J3JHmpZBsON2SNVob1Fvt2MQDw/GXOid1zgo/WKYYXP9SlR1UQt7rGbw3CcWHn3ZW/90so0mXW4wfFJedBQVguP5JRWNVvhtDhhnLtKkhCUcByJcM2lYoAsFWlIsBBNtsGzR14rrpJp8taDhgKikNEDnyzmIC1zIlGuGnZ2tUOwMkf4dbwi6sV16O8r+XiON2BHrYgAAw9uCIIyACwGWgbsGJ3a/RO2rDqHWmleloWRwS+oOq3UkhwQqZdBadNdR2YumKqq6LqimQtO5umgef2/dZHl8sOHDAUFEcOlooP7gjPYe/9pbwjaPnKn8JFcMKpWgDMc9MAeAd7wGX06WsAgE8ZeqRgCQr4L7AegCswYRvg2m3fgo6o2GTFmZoSEbeRx2MBIOLGl+p+y4WsTsi02+EhAET+O6CYqqlYAEgI61/MTpVkRjOb6OPxQ4a/DpcdOqAzKI6slMpdxAgbdywfD3G4I/xJBJAZ/dgMoAVOIqMAgG4hdu9VZqV/DAAJ/ScDAKLmA8g8FAJ80uStJAAjJbetNj0JFu2PzGAKJuI+gPpx0UDqoTKR5AbgXXL3BHr8XU1mfnSdoZmA+aPgwQCiECGbtNqTCVkHZdoFgxLMIyD9o6pTAcQh3N4UApclA+ZRpabaOSqdsWRTUG/ZsWUBft039VCkk+kyK1aZGXZQgj3ZkeRQQPdj5Y41PYqW6fQL0ei63v6BwZ9QRANfj8AedKWxr0dAqweza3p4VP+GiBaXmtL/ChFNrnTKTkd0i+ZLN094+QgRER1v9stna5b0+oOIKPXjZlMm9tom+/5rqSn9r9CVFoWs2qt9wxCMaF7YI7B1GsV2qr54wbDoJb4h54iIqm8johjpiwYiorRPO0wd98rETKKIFoU8AtqusLcnFRIHJdqtBm2YjOXDfpv/2rBkosMNfDyKB28nhZbpa6KHzZrdYVgSEckdlcxYsimovyTsSLwiOljX/pvFLJftYlU4wAyqga9HYA/lkeSQwZT930XMCC+v/rDg5LEndRoID/EpxTP9smc5661quGtpky49doKWy6BIn3JAins+ALhfCADiithJXXMp7dhviZB1UKZdhimjz1VLSAgyaZu6H2eTUKiSzGh6dfzkB/pcduiAjqA47GEinoOsYcroC0/lK1MfTfPmyX6W4P9QsgqCKadNbKl6Decr8krhpZKXkXZ5H9bF5LCRyERTyqzBPNnPFvwCLGs4NQ1AvqU5ayT9h+S0YfxXirxUODjyAvgFGAcHLxUODl4qHBy8VDg4eKlwcORZuOZu9x7NPloiuAOA5GW7vNt1z17lmbByAOYCkDk3ecNhj+z7VAlXfjF+fajOlZ+YTJ5W5DdZEAEAiR39hxXu8koMrrY1zZ/v/m22hn45f5EiUVnWEvN69ngzq0jh2llItv5sczgJ4+9Vti2p4vW5/Xc5okO2Kn/J17+1vo+Bi/WS1nW27piTbpw6+cd1jP0WwJi+QcDBtqU29lxaCcDKCvUNufpTpvDXvWTLAoxS6XnUskXLUmyjr5Yzlo6IEOH36rTElB/p6a2C8Hi1mxulNjb8xTCrJoepZiZbd7Y5nIXRryIfLBAzxv243XBao3/txpIbn9GncyEKRcoGzKuLlSMi+oqIiHa45P+biIjSpxrzdcciL7y/bfv2lUMLjHhkN3upnnVrL9B2zMLf160bipJGWa7Dqwt/M9ZNdUfxyTFET0bBrfOsaMNf8rZqcpRqdrL1Z5vDORgulTeaUa0Xk+2GZ/RjyG5tqlNpFzRJl49EldlPROOEnU/wqbDxnVFvu+Af4axzbZCiXiojSh4iIqKzvoXOZuEE/xgCf9bhyqedORR2paKSapVk6882x1MplYcun9KTNLvh+EKnWNLV1urTmlha4J2T4MSHRDSaiIhuNuiOuURER5cbDa87dlo3vlUvlWpHBTsl8odl5QS/bMoXQUS3g+84dSiUpaKSatVk6842h1Mwelt/LPMleLnZDYfWqMWSHvSzPq2FVrlO2i0feuklAO0WADjdbeGyNwdPzMS177s6fZ1ZG3+rzl1oVA8AEoPvLG+RlWvZim3N84DEfr8EIjugkmrVZOvONodTMFoqJ8A8TEvbM6Vb7b2mT23jseaesfKhDwG09H1/VMj3a2q6/TF/UdGaH8x0dzpOH43WE/uHAEBKhwszu2QtmYPxa/KTXtNLZ8+hUUm1arL1Z5vDGRh7r7LhySYcO12jpnI8/uSPtu3ry/wGumJflSIAqhTZrfOB0he79vTebP+wp1vXm/4+APL17x/nUjgLcZ5DOxlRvRQDAMD8zn+jhurVJo1RgvZlIhfvGVtZv1cJG6826kArL5V/11VvqqXJVizXn22OnC4VepR2OSgz0/6T6BBsPFZnWiXgQOi1JYsBAA32f6BPdb7QmltnDrcfN9n+RRfJSpgXlzUdhYz4ufc6HWjWLGIyQ2Lwhp6T9GqTxygJYtDnH++uo9+rq7O/6NbxfFKLVsER4/WmWpJsu+W6s82R06Viei998Ov9GBNRhW29PUavanlxV78j/wl7xSTkwr/Ml61xWS5781B8ScfRzetmf4CnXZEefer3Tz/3RKlRyRNXzYx5tQ1D7Ltf2i6Wf6hpuCuPUYK+X2TafzKqKkr/bpE7Xvn2u9bTzvbRnWox2fbLi13mJ3QuKRXgQupLlq1+iyvW8ctHK1MvlQLu+dokZlRCrcqfbLdcLPlLXoe//6r8lFFc0ncYOuedE9lPmXutGODafbLQDlEgqmdILf6mznrFHbSGu/IYJZha+fwvzZSDqopWvO0O3EnriQF1mqun+tqULY+rzamDsHfTGgx5DWKy7Zf7R4Ej52DsgdkS7Bc20gKWEhF967aNiGhwbdlTzgER1s2JhfXrTqmF3tn9gK87Vkt3J+M462ExbXYte5eI6JT+h+bWGKWPeCfOPgL3GN06osxE1LCyysNiW6ppJtYS0aPXLW9rrMlWLDeYbY4cflh80mR5KrN30PsAZn0XGgwAqdLLjtsfj7PdXZry69edf7WbW47/Z/BnDR7uWmhHMQCYoleNNEYb5qcOrd8gbaFuX0qagCfHWzhKNfoXmQg8+XyJ5Rbfmmz75UayzWEUBi/ATlawXCKd+ATA0hHzhDcdPg9EkfDJM8WmhA+KihOPo2WqXMopy3TXS3NyPF4PxtiVN7ClAgDsk/aS0HJXFqMVay9PB4a+98toxReENePen9HSUarhNeybrS1HjrWmUpps+XJptjmebanQaWsjwc8BbOg3aYCwV0o8emcXzHUHbt1sAgC4Lzl4KxbJdOX7TfGFwn+nHnwm/xXvtru/QWgwNvkH6HJXHqMFO3bPA9D1s1sbOsv1a8a9E80A/N5FI9XAkB/GbbRVijTZiuX3eankJAxdrl3FZHFnZ/5R1s2NiLdsXeydSkRpIZZGjsF9dOu+UfJg9l9f2t2r3LW7V3lYG78KA7Mq6lMqi9F6h7G1ZwYREX2NVnqdmzCDMsqXIKKbn9jfq8hSPRKS76xYk61YLmY7ZkM6v7N41vcqJ/GSbftwSC/b+4kmphPCRnwPzzc6z5jdsLKl2fTRl/WqTg4Z1ygHPjEg+w6AlahegrROp77rCwCXun/cWZdOZYwA8GBSx8HCdVdb7DmqM5lf/YXVhTMIGd+N0U51ygOPeeKMJdmM5ZZsM3oQcDztT5Uv8t23bp7z65pJlPyHsFdnkvC33zlK6YD8n5mF3QjTdb2q3xnKGj00afilK2PGX3Ww+OGENwdtJCJK+qVL71W24U61PYqW6TTXuishqhc/VSYgX63atWtX8QfcTuryVB5jeHWi0y/5FvYqeY6IqLNPgcLFmv2uR09irTnzRqYHD1o9+CrZf6pIUp0yMGoIDohTQrKVy8Vss3oQcGQZxkoluKF1K+KF4DQiWrZb2J1jefB6j4jMp22/DZnRUq/mKS2VFw29iGjnZDr7Yt/kFsNoRHcRyibflNBy3q4x+VvdpStN5yekrtfZ8EDysNgQ5DHafXXeAC5dJ6Jz4UxNYqpTh0TSDbc3xClrsuXLjWSbI2dLJY7MAdbr59vlXn5CRCmthAt0SvRl/QTJXH6dTt3bysUqRn77mojez6CL2Ec/XKKoSyLsfsLxZTgRHfCpcrXhJSKiFUdytFTkyEqpqGqSpjrl4xtE1Afib2DYyTaQbY6cLZXFpmUnvS13xfHVayUS0b23+1pnZ/ZlLNnaXKfuKyWUlwx/uJ8johSiXwtkMBbsrWfD+87+WDL3loo01bebnyciumzqJkoyk60/2xw5XCo9y1z64GfL9lt4rXfv7s29TLb2WekN/7Zb8aCWzt8UPqy6RlE6fVDDstm7HXNJhg1mZ38smXtLRUz1qfa+BZYQUUyIt0/vg1rJ1p9tDueg/73K10t/KjfQsr3ebtb1jw41la0/B4ypru/JQs+i3lus2ylP7kUcOUXoDgD3CyFsALCzRrFuV2ziphktFDxAyQCAqAPdpwUNBHCsTB5/1CKmupal+W/RPx0lW3e2OZ7KEzDNf4rDFQNrVulcyXxHH05Eu0wXdpnW0uPuZm0Fe+YT0anGp9PeNH2fQREhqfo+VfL5+NzIctgxb2RP+qb5eBn4fLJLtv5scziJ3NA0gtIYg/kBHB/YO6rZT10uDXf0C9w1W1647D6tFMy/TnpQosiS0s8+Jo7/O+Tu/iqZCQFIT9TxdQ0SfiwJIGs/luTgyJulwsGRa8DpvTk4eKlwcPBS4eDgpcLBwUuFg4OXCgcHLxUODg5eKhwcvFQ4OHipcHA8bfwPqGtMQdvJfCEAAAAASUVORK5CYII=" + } + }, "cell_type": "markdown", "metadata": {}, "source": [ - "# Problem 2" + "# Problem 3\n", + "![image.png](attachment:ec5948a6-fd01-4ab0-8c02-1093eb72f7a3.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can start by stating what $f_Z$ is:\n", + "$$\n", + "f_Z(z) = P(Z = z) \\\\\n", + "f_Z(z) = \\sum_{x = -\\infty}^\\infty P(X + Y = z | X = x) f_X(x) \\\\\n", + "f_Z(z) = \\sum_{x = -\\infty}^\\infty P(x + Y = z | X = x) f_X(x)\n", + "$$\n", + "\n", + "Fordi sandsynligheden af $x + Y = z$ ikke ændre sig når $X = x$ ændre sig, kan man sige følgende:\n", + "\n", + "$$\n", + "f_Z(z) = \\sum_{x = -\\infty}^\\infty P(x + Y = z) f_X(x) \\\\\n", + "f_Z(z) = \\sum_{x = -\\infty}^\\infty P(Y = z - x) f_X(x) \\\\\n", + "f_Z(z) = \\sum_{x = -\\infty}^\\infty f_Y(z - x) f_X(x)\n", + "$$" ] } ], @@ -165,7 +305,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.2" + "version": "3.8.9" } }, "nbformat": 4, |