From 7a6bc1648d8a5543dc6649bc8b07aeb367bebffd Mon Sep 17 00:00:00 2001 From: Kees van Kempen Date: Mon, 19 Sep 2022 22:16:33 +0200 Subject: [PATCH] 02: Complete the last, commit everything before hand-in --- Exercise sheet 2/exercise_sheet_02.ipynb | 75 ++++++++++++++++++++---- 1 file changed, 62 insertions(+), 13 deletions(-) diff --git a/Exercise sheet 2/exercise_sheet_02.ipynb b/Exercise sheet 2/exercise_sheet_02.ipynb index 201979f..34a7d83 100644 --- a/Exercise sheet 2/exercise_sheet_02.ipynb +++ b/Exercise sheet 2/exercise_sheet_02.ipynb @@ -203,7 +203,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -335,7 +335,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -429,7 +429,7 @@ "outputs": [ { "data": { - "image/png": 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qiIi1ed1eAM6KiH9KOg+oB07Paz87Il7twbrNzKyHJDkiqAFaImJ9ROwCFgJT8jtExFMR8c/c5nKgrGfLNDOz3pIkCAYDL+Vtt+b2deTfgd/lbQfwkKRVkuo6GiSpTlKjpMbNmzcnKMvMzHpCp0tDgArsi4IdpbNpC4Iz83aPj4iNkgYBf5D0XEQse98TRtTTtqREdXV1wec3M7Oel+SIoBUYkrddBmxs30lSJfBzYEpEbNm7PyI25v7cBCymbanJzMyKRJIgWAkMk1QuqR8wDWjI7yDpJOBe4PMR8Xze/v6SBux9DEwCVvdU8WZmduA6XRqKiN2SrgIeBEqA+RGxRtKsXPs8YA5wLPAfkgB2R0Q1cDywOLfvCGBBRPy+V96JmZl1S5JzBETEEmBJu33z8h5fAVxRYNx6YFT7/WZmVjz8yWIzs4xzEJiZZZyDwMws4xwEZmYZ5yAwM8s4B4GZWcY5CMzMMs5BYGaWcQ4CM7OMcxCYmWWcg8DMLOMcBGZmGecgMDPLOAeBmVnGOQjMzDLOQWBmlnEOAjOzjEsUBJImS1onqUXS7ALtMyU1536ekjQq6VgzM0tXp0EgqQS4HTgPqACmS6po1+0F4KyIqARuBOq7MNbMzFKU5DuLa4CW3PcPI2khMAVYu7dDRDyV1385UJZ0rNmhpKmpidra2rTLOCw0NTXBwCFpl2EkC4LBwEt5263A6fvp/+/A77o6VlIdUAdw0kknJSjL7ODqX1HLm2uXsnz9lrRLOTwMHEL/itq0qzCSBYEK7IuCHaWzaQuCM7s6NiLqyS0pVVdXF+xjlqYBVZMZUDU57TLMelySIGgF8o/fyoCN7TtJqgR+DpwXEVu6MtbMzNKT5KqhlcAwSeWS+gHTgIb8DpJOAu4FPh8Rz3dlrJmZpavTI4KI2C3pKuBBoASYHxFrJM3Ktc8D5gDHAv8hCWB3RFR3NLaX3ouZmXVDkqUhImIJsKTdvnl5j68Arkg61szMioc/WWxmlnEOAjOzjHMQmJllnIPAzCzjHARmZhnnIDAzyzgHgZlZxjkIzMwyzkFgZpZxDgIzs4xzEJiZZZyDwMws4xwEZmYZ5yAwM8s4B4GZWcY5CMzMMi5REEiaLGmdpBZJswu0D5f0tKS3JX2zXdsGSc9IapLU2FOFm5lZz+j0G8oklQC3A+fS9mX0KyU1RMTavG6vAVcD/9rB05wdEa8eYK1mZtYLkhwR1AAtEbE+InYBC4Ep+R0iYlNErATe6YUazcysFyUJgsHAS3nbrbl9SQXwkKRVkuo66iSpTlKjpMbNmzd34enNzOxAJAkCFdgXXXiN8RExGjgP+KqkCYU6RUR9RFRHRPVHPvKRLjy9mZkdiCRB0AoMydsuAzYmfYGI2Jj7cxOwmLalJjMzKxJJgmAlMExSuaR+wDSgIcmTS+ovacDex8AkYHV3izUzs57X6VVDEbFb0lXAg0AJMD8i1kialWufJ+kEoBEYCOyRdA1QARwHLJa097UWRMTve+WdmJlZt3QaBAARsQRY0m7fvLzHr9C2ZNTeG8CoAynQzMx6lz9ZbGaWcQ4CM7OMcxCYmWWcg8DMLOMcBGZmGecgMDPLOAeBmVnGOQjMzDLOQWBmlnEOAjOzjHMQmJllnIPAzCzjHARmZhnnIDAzyzgHgZlZxjkIzMwyzkFgZpZxiYJA0mRJ6yS1SJpdoH24pKclvS3pm10Za2Zm6eo0CCSVALcD59H2PcTTJVW06/YacDVwSzfGmplZipJ8Z3EN0BIR6wEkLQSmAGv3doiITcAmSZ/p6thC1q1bR21tbdL3YB1oamqCgUPSLsPMilySIBgMvJS33QqcnvD5E4+VVAfUAVDSl+XrtyR8CevQwCH0r6hNuwozK3JJgkAF9kXC5088NiLqgXqAD5w4LE6YcXPClzAzswOR5GRxK5C/vlAGbEz4/Acy1szMDoIkQbASGCapXFI/YBrQkPD5D2SsmZkdBJ0uDUXEbklXAQ8CJcD8iFgjaVaufZ6kE4BGYCCwR9I1QEVEvFFobC+9FzMz64Yk5wiIiCXAknb75uU9foW2ZZ9EY83MrHj4k8VmZhnnIDAzyzgHgZlZxjkIzMwyzkFgZpZxDgIzs4xzEJiZZZyDwMws4xwEZmYZ5yAwM8s4B4GZWcY5CMzMMs5BYGaWcQ4CM7OMcxCYmWWcg8DMLOMcBGZmGZcoCCRNlrROUouk2QXaJem2XHuzpNF5bRskPSOpSVJjTxZvZmYHrtOvqpRUAtwOnAu0AislNUTE2rxu5wHDcj+nA/+Z+3OvsyPi1R6r2szMekySI4IaoCUi1kfELmAhMKVdnynAf0Wb5cDRkk7s4VrNzKwXJAmCwcBLedutuX1J+wTwkKRVkuo6ehFJdZIaJTW++9bWBGWZmVlP6HRpCFCBfdGFPuMjYqOkQcAfJD0XEcve1zmiHqgH+MCJw9o/v5mZ9ZIkRwStwJC87TJgY9I+EbH3z03AYtqWmszMrEgkCYKVwDBJ5ZL6AdOAhnZ9GoBLc1cPnQFsjYiXJfWXNABAUn9gErC6B+s3M7MD1OnSUETslnQV8CBQAsyPiDWSZuXa5wFLgPOBFuAt4PLc8OOBxZL2vtaCiPh9j78LMzPrtiTnCIiIJbT9ss/fNy/vcQBfLTBuPTDqAGs0M7Ne5E8Wm5llnIPAzCzjHARmZhnnIDAzyzgHgZlZxjkIzMwyzkFgZpZxDgIzs4xzEJiZZZyDwMws4xwEZmYZ5yAwM8s4B4GZWcY5CMzMMs5BYGaWcQ4CM7OMcxCYmWVcoiCQNFnSOkktkmYXaJek23LtzZJGJx1rZmbp6jQIJJUAtwPnARXAdEkV7bqdBwzL/dQB/9mFsWZmlqIkRwQ1QEtErI+IXcBCYEq7PlOA/4o2y4GjJZ2YcKyZmaUoyZfXDwZeyttuBU5P0GdwwrEASKqj7WgC4O0X516wOkFtaToOeDXtIhJwnT3LdfYs19lzPtbdgUmCQAX2RcI+Sca27YyoB+oBJDVGRHWC2lJzKNQIrrOnuc6e5Tp7jqTG7o5NEgStwJC87TJgY8I+/RKMNTOzFCU5R7ASGCapXFI/YBrQ0K5PA3Bp7uqhM4CtEfFywrFmZpaiTo8IImK3pKuAB4ESYH5ErJE0K9c+D1gCnA+0AG8Bl+9vbIK66rvzZg6yQ6FGcJ09zXX2LNfZc7pdoyIKLtmbmVlG+JPFZmYZ5yAwM8u41IIgwW0raiVtldSU+5mTUp3zJW2SVPBzDfu7vUYR1VgsczlE0mOSnpW0RtLXC/QphvlMUmfqcyqpVNIKSf+Tq/O7BfqkOp8Ja0x9LvNqKZH0Z0n3F2hL/d9mXi37q7Pr8xkRB/2HthPHfwVOpu0S0/8BKtr1qQXuT6O+dnVMAEYDqztoPx/4HW2fmTgD+GMR1lgsc3kiMDr3eADwfIG/92KYzyR1pj6nuTn6UO5xX+CPwBnFNJ8Ja0x9LvNq+V/AgkL1pD2XXaizy/OZ1hHBIXPriYhYBry2ny4d3V7joElQY1GIiJcj4k+5x9uAZ2n79Hm+YpjPJHWmLjdH23ObfXM/7a/+SHU+E9ZYFCSVAZ8Bft5Bl9T/bUKiOrssrSDo6JYU7Y3NHVL+TtJpB6e0Lkv6XtJWVHMpaSjwCdr+h5ivqOZzP3VCEcxpbomgCdgE/CEiim4+E9QIRTCXwK3A/wb2dNCe+lzm3Mr+64QuzmdaQZDk1hN/Aj4aEaOAnwD39XZR3ZT4NhopKqq5lPQh4B7gmoh4o31zgSGpzGcndRbFnEbEuxFRRdun9mskjWjXJfX5TFBj6nMp6QJgU0Ss2l+3AvsO6lwmrLPL85lWEHR624qIeGPvIWVELAH6Sjru4JWYWJJbcKSqmOZSUl/afrneFRH3FuhSFPPZWZ3FNKe5Gl4HlgKT2zUVxXxCxzUWyVyOBy6StIG2pepPSfp1uz7FMJed1tmd+UwrCDq99YSkEyQp97iGtlq3HPRKO9fR7TWKRrHMZa6GXwDPRsQPO+iW+nwmqbMY5lTSRyQdnXv8QWAi8Fy7bqnOZ5Iai2EuI+LbEVEWEUNp+330aER8rl231P9tJqmzO/OZ5KZzPS6S3bbi34AvS9oN7ACmRe6U+MEk6Te0nYU/TlIr8H9oO+G1t86Ct9coshqLYi5p+9/M54FncmvGANcBJ+XVmvp8kqzOYpjTE4E71fYFUH2A/46I+5Xg9i9FVmMxzGVBRTaXHTrQ+fQtJszMMs6fLDYzyzgHgZlZxjkIzMwyzkFgZpZxDgIzs4xzEJiZZZyDwMws4/4f1QSTbeiJDgsAAAAASUVORK5CYII=\n", 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\n", 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\n", 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\n", 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" ] @@ -583,7 +583,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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" ] @@ -764,7 +764,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -850,7 +850,7 @@ "= \\frac{1}{2\\pi}\\, r\\,e^{-r^2/2}\n", "\\\\ \\implies f_{X}(x)f_Y(y) = \\frac{1}{2\\pi}\\,e^{-r^2/2} = \\frac{1}{\\sqrt{2\\pi}}e^{-x^2/2}\\frac{1}{\\sqrt{2\\pi}}e^{-y^2/2}\n", "$$\n", - "using that $r^2 = x^2 + y^2$ in the last step. We conclude that $X$ and $Y$ are independent, and that they are both distributed as a standard normal distribution $\\mathcal{N}(0,1)$" + "using that $r^2 = x^2 + y^2$ in the last step. We conclude that $X$ and $Y$ are independent, and the factorization shows that they are both distributed as a standard normal distribution $\\mathcal{N}(0,1)$." ] }, { @@ -874,9 +874,30 @@ "__(b)__ Write a function to sample a pair of independent normal random variables using the Box-Muller transform. Hint: to sample $R$ you can use the inversion method of the first exercise. Produce a histogram to check the distribution of your normal variables. __(15 pts)__" ] }, + { + "cell_type": "markdown", + "id": "36710a33", + "metadata": {}, + "source": [ + "For the sampling of $R$, we take its PDF, calculate its CDF, invert it, and use the function `inversion_sample` to pull values for $R$.\n", + "\n", + "$$\n", + "f_R(r) = re^{-r^2/2}\n", + "\\\\ \\implies F_R(r) = \\int_{-\\infty}^r te^{-t^2/2}dt = -e^{-r^2/2}\n", + "$$\n", + "which can be calculated using a substitution with $z := t^2$.\n", + "\n", + "Now the inversion.\n", + "\n", + "$$\n", + "p := F_R(r) = -e^{-r^2/2} \\implies r = \\sqrt{\\ln{p^2}}\n", + "$$\n", + "for $p \\in [0, 1]$." + ] + }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "id": "e4023f99", "metadata": { "deletable": false, @@ -892,17 +913,45 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", 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QuiIiklm9BnozKwDuAc4BSoGLzay0S7E/ASe5ewS4ArivD3VFRCSDgsyjrwC2unsDgJktB+YBm9sLuPvelPJFgAetK3I4UlMewOBIe9CdtbV1FE44sK/tXTddo5QI0i+CDN2MBXakHDcmz3ViZhea2avA4yR69YHrJutXJYd96nbv3h2k7SKdUh5A7qc96E5qOgRQSgTpX0F69Jbm3EE7irv7SmClmZ0G/Bg4O2jdZP0YEIPE5uAB2iUCQMvI8WyfcUPHcXEW23KoUtMhgFIiSP8K0qNvBFJ/Fx4H7OyusLuvBT5rZkf3ta6IiPS/IIF+PTDZzErMbDiwAFiVWsDMPmdmlnw9DRgONAepKyIimdXr0I27t5nZ1cCTQAGwzN03mdmi5PWlwFeBS83sI2AfMN/dHUhbN0OfRURE0giUvdLdVwOru5xbmvL6duD2oHVFRGTgaGWsiEjIKdCLiIScAr2ISMgp0IuIhJwCvYhIyCnQy6ATi8WIRqNEo9FO6Q/CJh6Pd3zOWCyW7ebIIKZAL4NOan6bwZrbpjdFpVEikQiQCPjKeyOHI9A8epFcE4lEqKmpAWDi4sez25gMKI5UUrPkbgCi0Wh2GyODngK9DEq1Dc2hDPAimaBAL5Kj2r/IdjU0M2PSqCy3RgYzjdGLiIScAr2ISMgp0IuIhJwCvYhIyCnQi4iEnAK9iEjIBZpeaWaVwJ0kdom6z92XdLl+CfD95OFe4Fvu/rfkte3AHuBjoM3dy/un6ZJPUufM72pozmJLRAafXgO9mRUA9wBzSGz2vd7MVrn75pRi24DT3f3fZnYOEANOSbl+hru/1Y/tljwSi8XYVX13x3Fr0zaGjynJYosGXnveG4CFCxdSVVWV3QbJoBJk6KYC2OruDe7eCiwH5qUWcPcX3P3fycNaYFz/NlPyWXV1Na1N2zqOh48pCWV+m+4o740criBDN2OBHSnHjXTurXf1n8AfUo4deMrMHLjX3ZWGT/ps+JgSjl24pPeCIVQcqWQ7lQC0NCzOcmtkMAoS6C3NOU9b0OwMEoH+1JTTs919p5mNAf5oZq+6+9o0dauAKoAJEyYEaJaIiAQRZOimERifcjwO2Nm1kJmVAfcB89y942mZu+9M/t0ErCQxFHQQd4+5e7m7l48ePTr4JxARkR4FCfTrgclmVmJmw4EFwKrUAmY2AXgE+Lq7v5ZyvsjMittfA3OBjf3VeBER6V2vQzfu3mZmVwNPkpheuczdN5nZouT1pcDNwCjgv80MDkyjPAZYmTw3FKh29ycy8klERCStQPPo3X01sLrLuaUpr68ErkxTrwE46TDbKCIih0ErY0VEQk6BXkQk5LTDlOSs1B2WROTQqUcvIhJy6tFLTkrNb5OPuW16kpr3BpT7RnqnHr3kpNT8NvmW26YnqXlvQLlvJBj16CVn5XN+m+6k5r0B5b6RYNSjFxEJOQV6EZGQU6AXEQk5BXoRkZBToBcRCTkFehGRkFOgFxEJOQV6EZGQU6AXEQm5QIHezCrNbIuZbTWzg5bimdklZlaf/POCmZ0UtK5Iu1gsRjQaJRqNEo/Hs92cQaM99000GiUWi2W7OZKDeg30ZlYA3AOcA5QCF5tZaZdi24DT3b0M+DEQ60NdESCR36Y9wEciEeW3CSA1943y3kh3guS6qQC2JrcFxMyWA/OAze0F3P2FlPK1wLigdUVStYwcz/YZNwBQnOW2DAapuW+U90a6E2ToZiywI+W4MXmuO/8J/OEQ64qISD8L0qO3NOc8bUGzM0gE+lMPoW4VUAUwYcKEAM0SEZEggvToG4HxKcfjgJ1dC5lZGXAfMM/dm/tSF8DdY+5e7u7lo0ePDtJ2EREJIEigXw9MNrMSMxsOLABWpRYwswnAI8DX3f21vtQVEZHM6nXoxt3bzOxq4EmgAFjm7pvMbFHy+lLgZmAU8N9mBtCW7J2nrZuhzyIiImkE2mHK3VcDq7ucW5ry+krgyqB1RURk4GhlrIhIyCnQi4iEnDYHl6yJxWKdVnLG43EYOb77CtKr9nQIAAsXLqSqqiq7DZKcoB69ZE1qygNQ2oPDVVQapWXkeGobmllbW6d0CNJBPXrJqkgkQk1NTcfxxMWPZ68xg1xxpJLiSCIdwq5qpUOQA9SjFxEJOfXoJatqG5rVixfJMPXoRURCToFeRCTkFOhFREJOgV5EJOQU6EVEQk6BXkQk5DS9UgZUatoDpTzIrNR0CKCUCPlMgV4GVHV1NWtr6xg+pgRGjlfKgwwpKo0yteXljuP2VBMK9PlJgV4G3PAxJRy7cEm2mxFqxZFKapbc3XGc2rOX/BNojN7MKs1si5ltNbODkmiY2RQze9HMPjSz67tc225mL5tZ3Mzq+qvhIiISTK89ejMrAO4B5pDY7Hu9ma1y980pxd4GrgX+o5u3OcPd3zrMtopIH6SmltjV0MyMSaOy2BrJpiA9+gpgq7s3uHsrsByYl1rA3ZvcfT3wUQbaKCIihyFIoB8L7Eg5bkyeC8qBp8xsg5npSZCIyAAL8jDW0pzzPvyM2e6+08zGAH80s1fdfe1BPyTxJVAFMGHChD68vYiI9CRIj74RSJ3sPA7YGfQHuPvO5N9NwEoSQ0HpysXcvdzdy0ePHh307UVEpBdBAv16YLKZlZjZcGABsCrIm5tZkZkVt78G5gIbD7WxIiLSd70O3bh7m5ldDTwJFADL3H2TmS1KXl9qZscCdcBIYL+ZXQeUAkcDK82s/WdVu/sTGfkkIiKSVqAFU+6+Gljd5dzSlNe7SAzpdPUecNLhNFAGv1gsxrW3JhbvtDZtS6yKlQG3traOwglTAbjrpmu0SjaPKKmZZFx1dTWtTduAxKpYpT0YeEWl0Y4v2NambR35hiQ/KAWCDAilPciu4kglxZFKAHZVH7S4XUJOPXoRkZBToBcRCTkFehGRkFOgFxEJOQV6EZGQU6AXEQk5Ta+UjOiaC11yS21Dc6d/o+1LvpLF1kimKdBLv4vFYuyqPrCNnVbD5p7Wpm2d5tPHJr2hlbIhpqEb6XepK2FBq2FzTeoqWdBK2XygHr1khFbC5q7UVbKglbL5QD16EZGQU6AXEQk5BXoRkZBToBcRCTkFehGRkAsU6M2s0sy2mNlWMzvoEb2ZTTGzF83sQzO7vi91RUQks3oN9GZWANwDnENiH9iLzay0S7G3gWuBOw6hroRALBYjGo0SjUaJx+PZbo70UTwe7/j3i8Vi2W6O9LMgPfoKYKu7N7h7K7AcmJdawN2b3H098FFf60o4VFdXs7a2jtqGZlpGjtcCqUGkqDRKJBIBEgFfi6fCJ8iCqbHAjpTjRuCUgO8fuK6ZVQFVABMmTAj49pJLtEhqcCqOVLKdxAKqlgaNroZRkB69pTnnAd8/cF13j7l7ubuXjx49OuDbi4hIb4IE+kZgfMrxOGBnwPc/nLoiItIPggT69cBkMysxs+HAAmBVwPc/nLoiItIPeh2jd/c2M7saeBIoAJa5+yYzW5S8vtTMjgXqgJHAfjO7Dih19/fS1c3QZxERkTQCZa9099XA6i7nlqa83kViWCZQXRHJXambkmhDknBQmmI5ZLFYrGMqXjweh5Hje64gg0LqpiTakCQclAJBDpnmzodP6qYk2pAkPNSjl8OiufPhkropiTYkCQ/16EVEQk6BXkQk5BToRURCToFeRCTkFOglsFgsRuGEqR1/1tbWZbtJkmFra+s6/ZsrhfHgpEAvgVVXV9PatK3jePiYEk2pDLHUqZag6ZaDmaZXSp9oOmX+SJ1qCZpuOZipRy8iEnIK9CIiIadALyIScgr00iNt+i2ptIn44KSHsdKj9sRlw8eUgBKX5bWi0ihTW14G6PjSV2bLwUGBXnqlmTYC2kR8MAs0dGNmlWa2xcy2mtlB/8KWcFfyer2ZTUu5tt3MXjazuJlphY2IyADrtUdvZgXAPcAcEpt9rzezVe6+OaXYOcDk5J9TgP9J/t3uDHd/q99aLSIigQXp0VcAW929wd1bgeXAvC5l5gH/zxNqgU+Z2Wf6ua0yQPQAVoLQg9nBI0igHwvsSDluTJ4LWsaBp8xsg5l1++TGzKrMrM7M6nbv3h2gWZIp2jlKelNUGqVl5HhqG5pZW1un1Ag5LsjDWEtzzvtQZra77zSzMcAfzexVd197UGH3GBADKC8v7/r+MsD0AFZ6op2oBpcgPfpGIHXX53HAzqBl3L397yZgJYmhIBERGSBBevTrgclmVgK8ASwAFnYpswq42syWk3gI+667v2lmRcAQd9+TfD0XuKX/mi8iuaC2oZmJix/vON6+5CtZbI101Wugd/c2M7saeBIoAJa5+yYzW5S8vhRYDZwLbAU+AC5PVj8GWGlm7T+r2t2f6PdPIYclFot1GmONx+Mwcnz3FUS6aG3a1mkIJzbpDS2myiHmnnvD4eXl5V5Xpyn3AyUajR5Y/ZpUVBrtlKJWpDt74k/w/uaajuPWpm2cNqOcmpqabutI/zOzDe5enu6aVsYKoIevcuiUtz73KamZiEjIKdDnKS2KkkzSYqrcoqGbPKWslJIpRaVR3t9cQ21Dc8cew3owm10K9HlM4/KSCVpMlXs0dJNHNFwj2bC2to7CCVMpnDBVwzhZokCfR6qrqzsCfCQS0XCNZFxRabRj2m5r0zblxMkSDd3kmZaR49k+4wYAirPcFgk/DePkBgX6ENOKV8k17bNx2i1cuFAPageAAn2IdZpZA5pdI1mVOhsH0IycAaRAHzKpvfh4PK6ZNZIz0q2gTe3hq3efOQr0IaP58TJYaL79wFGgDwH14mUw6vqgVr37zFGgH4S6PmRds2YNAJ8Yf6J68TIopfbuP9yxkTVr1nT6b1yB//AoTfEgkRrcOwX2JKUVlrDomvb4wx0bATj99NMBBf3u9JSmWIE+h/UU3BXYJV+kBn4F/e4ddqA3s0rgThI7TN3n7ku6XLfk9XNJ7DD1DXf/S5C66eRToO86DJOqPbi3/0f9cuFUBXfJaz0F/a7y7UvgsAK9mRUArwFzSGwCvh642N03p5Q5F7iGRKA/BbjT3U8JUjedwRjoewrYPUk3DJNKPXeR9LoO8QDMmDQKOLiT1BeD9QvicAP9TOD/uvuXk8c/AHD321LK3AvUuPvvksdbgCgwsbe66RQXF/vJJ58c5LNlXfvij3S9i/ZrvVEwF+lf6b4Egmj//7i949X+xTEYrFmz5rC2EhwL7Eg5biTRa++tzNiAdQEwsyqg/Wt075o1a7YEaFsmHQ281ddK7T2Jvvhwx0befvKXfa43gA7pXoSU7sUBob0X7QF/zY5eCh6QC/fiuO4uBAn0luZc118DuisTpG7ipHsMyJkcpmZW1923Y77RvThA9+IA3YsDcv1eBAn0jUBqJqxxwM6AZYYHqCsiIhkUJB/9emCymZWY2XBgAbCqS5lVwKWWMAN4193fDFhXREQyqNcevbu3mdnVwJMkpkguc/dNZrYoeX0psJrEjJutJKZXXt5T3Yx8kv6XM8NIOUD34gDdiwN0Lw7I6XuRkwumRESk/2grQRGRkFOgFxEJOQX6AMzsejNzMzs6223JFjP7qZm9amb1ZrbSzD6V7TYNJDOrNLMtZrbVzPJ281MzG29mz5rZK2a2ycy+m+02ZZuZFZjZX83ssWy3pTsK9L0ws/EkUjj8M9ttybI/Aie6exmJtBY/yHJ7Bkwylcc9wDlAKXCxmZVmt1VZ0wZ8z92/AMwAvpPH96Ldd4FXst2InijQ9+7nwP+hm4Ve+cLdn3L3tuRhLYk1EfmiAtjq7g3u3gosB+ZluU1Z4e5vticsdPc9JALc2Oy2KnvMbBzwFeC+bLelJwr0PTCzC4A33P1v2W5LjrkC+EO2GzGAukvxkdfMbCLwReClLDclm35BoiO4P8vt6FHe7zBlZk8Dx6a59F/AjcDcgW1R9vR0L9z998ky/0Xi1/cHB7JtWRY4lUe+MLNPAg8D17n7e9luTzaY2XlAk7tvMLNolpvTo7wP9O5+drrzZjYVKAH+lki3zzjgL2ZW4e67BrCJA6a7e9HOzC4DzgPO8vxagBEkDUjeMLNhJIL8g+7+SLbbk0WzgQuSadoLgZFm9lt3/1qW23UQLZgKyMy2A+Xunu0MdVmR3EDmZ8Dp7r472+0ZSGY2lMQD6LOAN0ik9lg4iFZ595vkJkMPAG+7+3VZbk7OSPbor3f387LclLQ0Ri9B/RIoBv5oZnEzW5rtBg2U5EPo9lQerwD/m49BPmk28HXgzOR/B/Fkj1ZymHr0IiIhpx69iEjIKdCLiIScAr2ISMgp0IuIhJwCvYhIyCnQi4iEnAK9iEjI/X92ak1yD3ykGAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "def random_normal_pair():\n", " '''Return two independent normal random variables.'''\n", - " # YOUR CODE HERE\n", - " raise NotImplementedError()\n", + " phi = rng.random()*2*np.pi\n", + " r = inversion_sample(lambda p: np.sqrt(-np.log(p**2)))\n", + " x, y = r*np.cos(phi), r*np.sin(phi)\n", " return x, y\n", "\n", "# Plotting\n", - "# YOUR CODE HERE\n", - "raise NotImplementedError()" + "pdf = gaussian\n", + "samples = np.array([random_normal_pair() for _ in range(100000)])\n", + "for index in [0, 1]:\n", + " compare_plot(samples[:,index], pdf, -5, 5, 100) " ] } ],