{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Normaalijakauma

\n", "\n", "Tähtitieteen tutkimusta haittasivat 1600-luvulla epätarkat mittaustulokset esimerkiksi taivaankappaleiden etäisyyksiä, sijaintia ja liikkeitä mitattaessa. Epätarkkuus johtui mm. mittauslaitteiden kehittymättömyydestä ja inhimillisistä tekijöistä. Jo Galileo Galilei tuli tulokseen, että mittausvirheet noudattavat symmetristä jakaumaa ja että pieniä virheitä esiintyy useammin kuin suuria. Gauss niminen saksalainen matemaatikko ja tähtitieteilijä esitti vuonna 1809 lausekkeen jakaumalle, jota mittausvirheet noudattivat. Nykyään kyseistä jakaumaa kutsutaan normaalijakaumaksi.\n", " \n", "Normaalijakauman lauseke määrittelee funktion, jolla on seuraavia ominaisuuksia:\n", "" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'Satunnaismuuttuja x')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = -3\n", "x_max = 3\n", "\n", "loc = 0 \n", "scale = 1\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.40)\n", "plt.title('Normaalijakauma')\n", "plt.xlabel('Satunnaismuuttuja x')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On tärkeää huomata, että normaalijakauman yhteydessä ei ole mielekästä puhua yksittäisen satunnaismuuttujan arvon todennäköisyydestä. Normaalijakaumaa noudattava satunnaismuuttujahan on jatkuva eli voi saada mitä tahansa arvoja tietyltä väliltä. Tällöin yksittäiseen arvoon liittyvä todennäköisyys on ainakin teoreettisesti ajatellen 0. Yksittäisten arvojen todennäköisyyksien sijasta on mielekästä puhua kertymätodennäköisyyksistä ja kertymätodennäköisyyksien avulla voidaan edelleen laskea erilaisten välien todennäköisyyksiä.\n", "Käytännössä normaalijakaumaa hyödynnetään kertymätodennäköisyyksien avulla. Satunnaismuuttujan arvoon x liittyvä kertymätodennäköisyys on kohdan x vasemmalle puolella oleva käyrän alapuolelle jäävä pinta-ala.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = -3\n", "x_max = 3\n", "\n", "loc = 0 \n", "scale = 1\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.40)\n", "plt.title('Kertymätodennäköisyys')\n", "plt.xlabel('Satunnaismuuttuja x')\n", "\n", "x1 = -3\n", "x2 = -1\n", "r1 = np.linspace(x1, x2, 30)\n", "r2 = norm.pdf(r1, loc, scale)\n", "plt.fill_between(r1, r2, color='C0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Esimerkki. Älykkyysosamäärää voidaan mitata tarkoitusta varten laaditulla testillä. Testin pisteytys on skaalattu sellaiseksi, että amerikkalaisten älykkyysosamäärä noudattaa likimain normaalijakaumaa N(100,16). Merkintä N(100, 16) tarkoittaa normaalijakaumaa, jonka odotusarvo on 100 ja keskihajonta 16." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.10564977366685535" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "loc = 100\n", "scale = 16\n", "norm.cdf(80, loc, scale)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = 50\n", "x_max = 150\n", "\n", "loc = 100\n", "scale = 16\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.030)\n", "plt.xlabel('Älykkyysosamäärä')\n", "\n", "x1 = 50\n", "x2 = 80\n", "r1 = np.linspace(x1, x2, 30)\n", "r2 = norm.pdf(r1, loc, scale)\n", "plt.fill_between(r1, r2, color='C0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yllä on laskettu älykkyysosamäärään 80 liittyvä kertymätodennäköisyys. Tämän mukaan noin 10,6 % amerikkalaisista on älykkyysosamäärältään alle 80. Vastaavasti noin 89,4 % amerikkalaisista on älykkyysosamäärältään yli 80.\n", "\n", "Todennäköisyys, että henkilön älykkyysosamäärä on täsmälleen 80, on ainakin teoreettisesti ajatellen 0. Käytännössä näin ei ehkä ole, koska älykkyysosamäärätestin pisteytys ei ole mielivaltaisen tarkkaa. Jos esimerkiksi testi pisteytetään pisteen tarkkuudella, niin todennäköisyys älykkyysosamäärälle 80 on varmasti selvästi nollasta poikkeava. Normaalijakaumaa käytettäessä kuitenkin oletetaan yksittäiseen satunnaismuuttujan arvoon liittyväksi todennäköisyydeksi 0.\n", "\n", "Todennäköisyys, että henkilön älykkyysosamäärä on välillä 80 - 110 saadaan selville vähentämällä arvoon 110 liittyvästä kertymätodennäköisyydestä arvoon 80 liittyvä kertymätodennäköisyys: " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6283646972844441" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm.cdf(110, loc, scale) - norm.cdf(80, loc, scale)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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2azKxLW8X+u2/mMVR/Df3ON/RlD91Doe03jDj37BxafH1TUKxBGBi27Q3kO2reS6/O4nW13+JObM/JFWAjKd8R2JijCUAE7tytqM/PMdk2vNt3jG+oym/aqRCx1sh80NYN893NCaGWAIwsWvyK8jOjcHevzkkp/8VKtWA8XY1kNnLEoCJTbs2oxNf5mtNY2peS9/RlH9V68Jpt8OCz2DVT76jMTHCEoCJTZMGIznbeDG8z+0l5mB1/BNUqWPnAsz/WAIwsWfnJnTyYMZpR2bnNSu+volO5ZruKGDxOMia7jsaEwMsAZjYM2kg5O5gYH4335HEn1P6QNV6kPGk70hMDLAEYGLLjo3o5Ff5PNyJzFChQ0SYQ1GpBpx2Byz5ClZM8R2N8cwSgIktE1+EvJ0MDF/tO5L4dcotULU+ZDzhOxLjmSUAEzuyf0WnDuWz8GnMCzX2HU38qlgNzvgbLMuAXyb6jsZ4ZAnAxI6JL6F5uxkcvsp3JPEv7Wao1sCuCEpwlgBMbNixAZ32OmPCpzI/1Mh3NPGvYlU4/Q74+VtYMdl3NMYTSwAmNkx8GfJ22d5/WUr7Q3AuwI4CEpUlAOPfjo3o1KGMtb3/slWxmjsKWDYeVk71HY3xwBKA8W/SQMjbySDb+y97J/8xuC/AjgISkSUA49fOTejU1/ivdrIrf3yoWM3dHbz0a7s7OAFZAjB+TR6M5O5gcL7t/Xtz8i1Qpa4dBSQgSwDGn12b0SmvMk472l2/PlWqDqf1hSVfWk+hCcYSgPFnymtIznbb+48FJ98ClWvDd//yHYkpQ5YAjB+7t6GTB/O1pjErZD1+ele5JnS6DRaOhTWzfUdjyoglAOPH1CHI7q0Mtj5/YkfHW6FSTTsKSCCWAEzZy8lGJw3iOzrwY97hvqMxe1Sp7ZLA/HQbOzhBWAIwZW/6G8iuTdb2H4s63QYVq8P3z/iOxJQBSwCmbOXuRCe+zCSOY3Lekb6jMQVVretuDpvzMfy6yHc0ppRFlQBEpIuILBSRJSIyoJDplURkRDB9ioi0CMrrich4EckWkYEF5skIljkzeDQoiQ9kYtyPbyM7frW9/1h22u2QUhm+f9Z3JKaUFZsARCQZGARcDLQBeohImwLVbgY2q2or4Hng6aB8N/AA0L+IxfdU1ROCx/qD+QCmHMnbjU54kWm05fu8o3xHY4pSrT6cfDNkfgiblvmOxpSiaI4ATgGWqOoyVc0FhgNdC9TpCrwTPB8JnCcioqo7VPUHXCIwiW7GMCR7rfX4WR6cdjskpcD3z/mOxJSilCjqNAFWRrzOAjoWVUdVQyKyFagHbChm2W+JSD7wEfCYqmrBCiLSB+gDkJqaSkZGRhQhl57s7GzvMcSKA1kXEs6j45Sn2Fy5NSc2bcWJEird4MpYahXo197/Z6qbvIqMjE0lsqxWDc+n8cz3mFLpLHIqR99Ca7+RvWJ9XUSTAKSQsoIb6mjqFNRTVVeJSA1cArgBeHefhagOAYYApKWlaefOnYsNuDRlZGTgO4ZYcUDr4se3IWcD/wjfwhdzKpRmWF70ax/i2cxofk6l69q0JvTsfFzJLKxDK3jxC04NTYLOz0c9m/1G9or1dRFNE1AWEHmrZlNgdVF1RCQFqAXsdzdEVVcFf7cD7+Gamkw8ys9Dv3+OeXIkX+S28x2NiVatptChJ8z4N2wr+JM38SCaBDANaC0iLUWkItAdSC9QJx3oFTzvBnxTWHPOHiKSIiL1g+cVgEuBOQcavCknMj9EtvzCoPyrKPxg0cSsM+6EcD5MeNF3JKYUFJsAVDUE9AXGAfOBD1R1rog8IiKXB9XeAOqJyBLgLuB/l4qKyHLgOeAmEckKriCqBIwTkdnATGAVMLTkPpaJGeF89LtnWCwtGJN7gu9ozIGq0wKO7+Ga8Lav8x2NKWFRNVqq6lhgbIGyByOe7wauKWLeFkUs9qToQjTl2pyPkU1LeTl8F7b3X06deRfMeg8mvgQXPe47GlOC7E5gU3rC+eh3/2KZNGd07om+ozEHq96R0P5amP4mZP/qOxpTgiwBmNIz71Nkw0IG5l+F2letfDurP+TtcuM3m7hhv0pTOsJh9Lt/8Ys05ZPcNN/RmENVvzW0uwqmvQ47S+Y+A+OfJQBTOhaOQdbPY1D+FYTtaxYfzrobcrNh8mDfkZgSYr9MU/JU0W+fJksa81FuwZvGTbnV4Fho0xWmvAa7NvuOxpQASwCm5C0ci6zNZFD+FeST7DsaU5LOugdytsHkV3xHYkqAJQBTslTRjKdYndSID3JP9R2NKWkN28Gxl8HkV2HXFt/RmENkCcCUrEX/RdbO5uWQ7f3HrbPvhZytMOVV35GYQ2QJwJQcVTTjSVYnNeSD3NN8R2NKS8P2cMylMGmwHQWUc5YATMlZNA5ZM4uBtvcf/86+JzgKeM13JOYQWAIwJUMV/fYp1iSl2t5/Imh0PBz9O5g8CHZv9R2NOUiWAEzJWPwFsnoGg0JXEIquiylT3nW+1238J9u5gPLKEoA5dKro+MdZndSQ4bmn+47GlJVGxwfnAgbZuYByyhKAOXQLxyJrZvFS6Crb+080nQe4cwF2d3C5ZAnAHJpwGB3/BFlJjfnQrvtPPA3bu7uDJw22PoLKIUsA5tAsGI2sm8NLoavsyp9EdfYA10eQ9RRa7lgCMAdPw+j4J/lFmjIyt5PvaIwvqW1cT6GTX4UdG31HYw6AJQBz0A77dQLy63xeyr/KevxMdGffC3k7YcILviMxB8B+tebg5Ido+fP7LJNmjMo9xXc0xrfDjob218DUoVTMsZ5CywtLAObgzB5O1V2reD7/Otv7N07nARDOo/mKD31HYqJkv1xz4EI5kPE06ysfwejcDr6jMbGi3pHQ4fc0Xj0OtqzwHY2JgiUAc+B+fAe2rmBK/WsA8R2NiSVn3QMIZDztOxITBUsA5sDk7oDv/gWHn0FW1Xa+ozGxplYTVjW5GGa9BxsW+47GFMMSgDkwU4fAjvVw3gMgtvdv9rWi+dWQUgXGP+47FFMMSwAmeru2wA8vQOsLobld928Kl1exNpx6G8wdBWtm+Q7H7IclABO9CS+43h/PfcB3JCbWnXY7VKkDXz3kOxKzH5YATHS2rXZ3era/Bhod5zsaE+sq14Iz+8PSb2BZhu9oTBGiSgAi0kVEForIEhEZUMj0SiIyIpg+RURaBOX1RGS8iGSLyMAC85wkIpnBPC+JWINyTMt4CsIhOPd+35GY8uLkP0KtZvDlPyAc9h2NKUSxCUBEkoFBwMVAG6CHiLQpUO1mYLOqtgKeB/ZcA7YbeADoX8iiXwH6AK2DR5eD+QCmDPy6CGYMcz/oOi18R2PKiwqV4Zz7Yc1MmPeJ72hMIaI5AjgFWKKqy1Q1FxgOdC1QpyvwTvB8JHCeiIiq7lDVH3CJ4H9EpBFQU1UnqaoC7wJXHMoHMaXom0egQjU4q7A8bsx+HHctNGgL3zwK+Xm+ozEFRDN6RxNgZcTrLKBjUXVUNSQiW4F6wIb9LDOrwDKbFFZRRPrgjhRITU0lIyMjipBLT3Z2tvcYylLNrQs5cf5ofm7Rk1+mzfnNtPqVwvRrb4f2AKlVoF/7kO8wqJu8iowMv/3yF/yN1E29iuMyH2XR8PtZ3eQSf4F5EOvbi2gSQGFt83oQdQ6qvqoOAYYApKWlaefOnfez2NKXkZGB7xjKjCq88ThUT6Vlj3/SslL130x+5f3RPJtp1xGA2/g/m+l/NLRr05rQs7Pfk/T7/Eb0bNiewVGrPuKoq+93J4gTRKxvL6L59WYBzSJeNwVWF1VHRFKAWsD+dkOyguXsb5nGt7mjIGuqu+yzwMbfmKiJwIWPwc6N8P1zvqMxEaJJANOA1iLSUkQqAt2B9AJ10oFewfNuwDdB236hVHUNsF1EOgVX/9wIfHrA0ZvSk7fbXcOd2g5OuN53NKa8a3wCHN8dJr8Cm3/xHY0JFJsAVDUE9AXGAfOBD1R1rog8IiKXB9XeAOqJyBLgLuB/l4qKyHLgOeAmEcmKuILoz8DrwBJgKfB5yXwkUyKmvgZbfnF7bkk21KMpAec+AJIEXz/sOxITiKrRUlXHAmMLlD0Y8Xw3cE0R87Yoonw6YL2JxaIdG+G7Z6H1RXDkOb6jMfGiVhN3h/B3/4ROt0HTNN8RJTw7g2f2lfGkG+T7wkd9R2Lizel/heqpMO7/3EUGxitLAOa31s2F6W9CWm83zJ8xJalSddcUtHIKZI70HU3CswRg9lKFz++FyjXdHZzGlIYTekLjDvDlA5CT7TuahGYJwOw171NY/j2c+3eoWtd3NCZeJSXBxf+E7Wvg+2d9R5PQLAEYJ3cnfPF3SG0PJ/X2HY2Jd81OgeN7wKSBsHGp72gSliUA40x4EbauhIuftss+Tdk4/yFIrgjjrLnRF0sABjYvd4O9tLsaWpzuOxqTKGo0hLPvgUWfw6IvfEeTkCwBJDpVGNMfklLgArvs05Sxjn+G+kfD2P6uGdKUKUsAiW5+Oiz5Es75P3ejjjFlKaUi/O5Zd9f598/4jibhWAJIZDnb4fMB7sTvKbf6jsYkqpZnuhPCE16C9Qt8R5NQLAEksvFPukvxLnsBkv13ZWwS2AWPQsVqMOYuu0O4DFkCSFRrZsOUV9wdv9Yni/Gt+mFwwcPwywSY+Z7vaBKGJYBElB+C9Nuhaj0478Hi6xtTFjrcCM06whf3Q/Z639EkBEsAiWjSy26g7kuegSp1fEdjjJOUBJe/DLk7YOzdvqNJCJYAEs2Gxa7t/9jLoO0VvqMx5rcOO9rdGzDvE5g/2nc0cc8SQCIJh+HTvlChClxifbCYGHX636BhexjTD3Zt9h1NXLMEkEimDYWVk6HLU1Aj1Xc0xhQuuQJ0HQQ7Nlg3EaXMEkCi2LjUjfHb6nw3NqsxsazR8XDG32Dmf2Dhf31HE7csASSC/BB83Md1vHX5yyDiOyJjinf2vZDaDtL7uqMBU+IsASSCH56HVdPh0uegZmPf0RgTnZRKcNUQ2L0VRv/VbhArBZYA4t2qn+Dbp6D9Na63T2PKk9S27l6VBZ/ZDWKlwBJAPMvdCaNudYNwX/Iv39EYc3A6/QVanOmGK9283Hc0ccUSQDz77wDYsMhdUWE3fJnyKikJrhjszl2NvBny83xHFDcsAcSrzJHw0ztwxl1w5Dm+ozHm0NRuDpe/5M5lff2w72jihiWAeLRxqTtp1qwTnGPXUZs40fZKSLsZJr4Mi8b5jiYuWAKIN6Ec+PAmdzNNtzesm2cTXy56wo1fMepPsHWV72jKPUsA8ea/98Ha2XDFK1Crqe9ojClZFSrDNW9Dfi6M/AOEcn1HVK5FlQBEpIuILBSRJSIyoJDplURkRDB9ioi0iJh2X1C+UEQuiihfLiKZIjJTRKaXxIdJeD8Ng+lvwGl3wNEX+47GmNJRv5U7H7ByMoz7P9/RlGvFtg+ISDIwCLgAyAKmiUi6qs6LqHYzsFlVW4lId+Bp4DoRaQN0B9oCjYGvROQoVc0P5jtHVe0Wv5KQ9aMbTemIznDeP3xHY0zpanc1rJ7hzgc0PgE6/N53ROVSNEcApwBLVHWZquYCw4GuBep0Bd4Jno8EzhMRCcqHq2qOqv4MLAmWZ0rS9nUw4vdQoxF0e8va/U1iOO8ht8Pz2Z1uB8gcsGgSQBNgZcTrrKCs0DqqGgK2AvWKmVeBL0TkRxHpc+ChGyA46dvLdZvb/T9Qta7viIwpG8kpboenRkO3A7R9re+Iyp1odhUL6zmsYKccRdXZ37ynq+pqEWkAfCkiC1T1u33e3CWHPgCpqalkZGREEXLpyc7O9h7D/6hyzIIXaLhuEnPb9OfXBRthQUaZvX39SmH6tQ+X2fvFstQq0K99yHcY1E1eRUbGJq8xlPVvpFqruzjxpwHsfO0SZnR4gnBy5TJ77+LE1PaiENEkgCygWcTrpsDqIupkiUgKUAvYtL95VXXP3/UiMgrXNLRPAlDVIcAQgLS0NO3cuXMUIZeejIwMfMfwP+OfgHUZcO7faXtW2Q+h98r7o3k20y4kA7fxfzbTf9PbtWlN6Nn5OK8xlP1vpDO0bkSN4T04a/07cN2/ISm5DN+/aDG1vShENL/eaUBrEWkpIhVxJ3XTC9RJBzVTi38AABE9SURBVHoFz7sB36iqBuXdg6uEWgKtgakiUk1EagCISDXgQmDOoX+cBDLzPfj2aXfy68z+vqMxxq+ju0CXp2HhWLsy6AAUu8uiqiER6QuMA5KBN1V1rog8AkxX1XTgDWCYiCzB7fl3D+adKyIfAPOAEPAXVc0XkVRglDtPTArwnqraqA/RWjoe0u9wJ8AufcH69zcGoGMf11nc5EGu64hT/+I7opgX1TGrqo4FxhYoezDi+W7gmiLmfRx4vEDZMuD4Aw3WACunwvDrof5RcO277o5fY4xz4aOwdaU7CqhUE068wXdEMc0acMuTtZnwn27uqocbRkHlWr4jMia2JCXD1a/DkefC6Dtg7ijfEcU0SwDlxYYlMOxKqFgDbvzUBnU3pigpldyJ4KanwEe3wOKvfEcUsywBlAcbFsM7l7kh8W78xLVvGmOKVrEaXD8CGhwDI3rCkq99RxSTLAHEuvUL4K1LXOdXvdKhfmvfERlTPlSpDTd8CvVaw/vdrQvpQlgCiGVr58DbvwNJgt5j3fioxpjoVavndpxS28LwnjB/tO+IYoolgFi1chq8c6lrz+w9Fg472ndExpRPVeu682aNT4APesGsEb4jihmWAGLRgjFu41+5Ntw0Buod6TsiY8q3yrXclXOHnwaj+sD3z7lzagnOEkCsmfa669iqQRu4+Uuo29J3RMbEh0o14PcfQbtublzhMf0gnF/8fHHMf+clxskPwVf/gEkD4agu0O1NdyWDMabkpFSCq4ZCrSYw4UXYtsq9rlzTd2Re2BFALNi5yd3gNWkgnPxHuO4/tvE3prQkJcEFj8Alz8DiL+H189yl1gnIEoBv6+bC0HPglwlw2Uvwu2dtQBdjysIpt7iTwzs3wtBzYeHnviMqc5YAfFGFH9+GoedB3m64aSyc1KvY2YwxJajlmdDnW3eu7f3u8MUDCTXQvCUAH3Zthg9uhNF/heYd4dZvodnJvqMyJjHVbgZ/GAdpf4CJL8GbF8LGpb6jKhOWAMra0vHwyhmu3/ILHoHfj3Kduxlj/KlQBS59Hq4dBpt+htfOckfocX6pqCWAsrJrM3z6Fxh2BVSoDDd/Aaf/1Z2QMsbEhjaXw58nQOMO7gj93ctdQohTtvUpbaow9xMY1BFmvg9n3Al/mgBNTvIdmTGmMLWawo3pbrClVTNg8Kkw8WXIz/MdWYmzBFCa1s5xvXh+2AuqN4BbvoHzH3JHAMaY2JWUBGm94S9T3Mh7X/wdXjkt7rqWtgRQGravhc/uhNfOhHVz3KWdt2S4vkiMMeVHrSbQ433oMQLCIfjP1fDedbBunu/ISoRdcF6SdmyACS/A1KHucPHkW6DzANcZlTGmfBJxg84feQ5MeQ2+/ac7GmjfDc4eAPVb+Y7woFkCKAlbV8GUV2DamxDaBcddB2ffA3WP8B2ZMaakpFSC0++ADr933UhMHQJzPob218Bpt0PDdr4jPGCWAA7F2kyYOBDmjAQNQ9sr4ex7retmY+JZ1bpwwcNw6l/ghxfc5aKzh8OR58FpfaFl53JzdZ8lgAOUlJ8DM/7t/ulZ06BCNdd/T6fboM7hvsMzxpSV6g2gyxNwVn+Y/qZrHhp2pTvyP+kmOKGn7wiLZQkgGuF8WP49ZH7IabM/hvydUP8ouOhJOL67tfEbk8iq1nVJ4NS+MO9T+PEt+PJB+PpR2tY9EQ7bAkdd5G42izGWAIoSyoVffnAdRM1Lh+y1ULE6G+p3pOHFd7uBJUR8R2mMiRUVKsPx17nH+vnw07vU/Ol9dxl4xRpwzCVw9CXQ6jw3NkEMsAQQafMvsCwDln7jHjnbIKWK+4e17wZHdWHBhCk0bHG670iNMbGswbHQ5UkmVTqfzocnw+wPYeEYmD0CkitCizPhyHPdlUUN2njbmUzcBBAOw8bFsGIyrJzqumPeHNzyXaMRtL3CZeuWZ0PFqn5jNcaUT5LsbiQ7ojPkvwgrp7h+wBaNgy/ud3WqNXAtCs07QbNToOFxkFyhTMJLjAQQynUb+/XzYc1MWD0T1syGnK1uepW60PxU6PRn94+qf5Q17xhjSlZyCrQ43T0uetxdPv7zt67V4ZdJMO8TVy+lMqS2czeONjoBUtvAYceUyiBR8ZMA8vNgaxZsXQmblrnuXDctcyP9bFrq7uIDSK4EqW2h3VWuP57mnaBeK9vgG2PKVq0mcML17gEuIaycAlnTYc0smDXCjRG+R+3D3c5pvSOh7pHuaqPazV131gd5gjmqBCAiXYAXgWTgdVV9qsD0SsC7wEnARuA6VV0eTLsPuBnIB+5Q1XHRLLNQu7fCT+/Cjl9h+zrYvtp1u7BtNWxf467F3yO5ItRp6Tbux17m2uQOO8Zdo19Gh1fGGBO1Wk2g1lVu5xRcM/Xmn13Lxfr5sH6ea8n4ZSLk7fjtvNUOg5qNoUZjqNkIqjeE6oe58mqHFfmWxSYAEUkGBgEXAFnANBFJV9XIzjBuBjaraisR6Q48DVwnIm2A7kBboDHwlYgcFcxT3DL3tWkZpN/unleq6drqazSElmdBrWZ7s2Gdlq5Hv6Tk4j6eMcbEpqQkt7df70g49tK95aqQvc5tD7eshK0rYMsK2LbGtYBkTXXDXEYhmiOAU4AlqroMQESGA12ByI11V+Ch4PlIYKCISFA+XFVzgJ9FZEmwPKJY5r4OOxr+Ng6q1Y/Ja2qNMabUibgd3xoNoah7T0O5Lgns+BV2rIeHLyi0WjQJoAmwMuJ1FtCxqDqqGhKRrUC9oHxygXmbBM+LWyYAItIH6BO8zJY6zRdGEXNpqg9s8BxDTEiqWrttcvW61p4G3LlrmyRVqel9+KjnBm1Z869rNq3zHIb9RvaKlXVRaKqIJgEUdna04Be9qDpFlRfWUUahPx5VHQIM2V+AZUlEpqtqmu84YoGITM/fsdnWBW5dhLb9ausC+41EivV1EU2PRVlAs4jXTYHVRdURkRSgFrBpP/NGs0xjjDGlKJoEMA1oLSItRaQi7qRueoE66UCv4Hk34BtV1aC8u4hUEpGWQGtgapTLNMYYU4qKbQIK2vT7AuNwl2y+qapzReQRYLqqpgNvAMOCk7ybcBt0gnof4E7uhoC/qGo+QGHLLPmPVypipjkqBti62MvWxV62LvaK6XUhbkfdGGNMoikfoxYYY4wpcZYAjDEmQVkCKIaI1BaRkSKyQETmi8ipIlJXRL4UkcXB3zq+4ywLInKniMwVkTki8r6IVA5O5E8J1sWI4KR+3BGRN0VkvYjMiSgr9HsgzksiskREZovIif4iL3lFrIt/Bb+R2SIySkRqR0y7L1gXC0XkIj9Rl47C1kXEtP4ioiJSP3gdc98LSwDFexH4r6oeAxwPzAcGAF+ramvg6+B1XBORJsAdQJqqtsOdvN/T7cfzwbrYjOsWJB69DXQpUFbU9+Bi3BVvrXE3Mb5SRjGWlbfZd118CbRT1eOARcB9AAW6g+kCDA66l4kXb7PvukBEmuG6ulkRURxz3wtLAPshIjWBs3BXOaGquaq6BddtxTtBtXeAK/xEWOZSgCrBvR5VgTXAubjuPyCO14Wqfoe7wi1SUd+DrsC76kwGaotIo7KJtPQVti5U9QtVDbrcZTLu3h6I6A5GVX8GIruDKfeK+F4APA/cw29vcI2574UlgP07AvgVeEtEZojI6yJSDUhV1TUAwd8GPoMsC6q6CngGt0ezBtgK/AhsifjhR3b1kQiK+h4U1n1KIq2XPwCfB88Tbl2IyOXAKlWdVWBSzK0LSwD7lwKcCLyiqh2AHSRAc09hgvbtrkBLXM+u1XCHtAXZdcXRdZ8Sl0Tkftw9P//ZU1RItbhdFyJSFbgfeLCwyYWUeV0XlgD2LwvIUtUpweuRuISwbs+hW/B3vaf4ytL5wM+q+quq5gEfA6fhDmP33FCYaF16FPU9SMiuTkSkF3Ap0FP33mCUaOviSNxO0iwRWY77vD+JSENicF1YAtgPVV0LrBSRo4Oi83B3NUd2fdEL+NRDeGVtBdBJRKoGXX3vWRfjcd1/QOKsiz2K+h6kAzcGV310ArbuaSqKV8EAT/cCl6vqzohJRXUHE5dUNVNVG6hqC1VtgdvonxhsS2Lve6Gq9tjPAzgBmA7MBj4B6uC6uv4aWBz8res7zjJaFw8DC4A5wDCgEu48yVTcyb0PgUq+4yylz/4+7txHHu5HfXNR3wPcof4gYCmQibtyyvtnKOV1sQTXvj0zeLwaUf/+YF0sBC72HX9pr4sC05cD9WP1e2FdQRhjTIKyJiBjjElQlgCMMSZBWQIwxpgEZQnAGGMSlCUAY4xJUJYATMwRkYlBL6xjfcdiTDyzy0CNMSZB2RGAiTkicmXQj/pJwesWhfW3XmCeh0SkfyHlGSKSVlqxlhURuVxEBojIjSLyp4jytKCP+fODcbr3tww7sjK/Ueyg8MZ40B34AbgO1+NowlPVdFxXAgXLp+PuVAf4qrB5RSRFVUOqelpQdEnpRGnKGzsCMDEl6G77bFz3AtcE/Q5FTv9eRE6IeD1BRI4rUOcWEflcRKpElCWJyDsi8piI3Cwizxeo/5yIPCoif40of1xE7hCRRiLynYjMFDca2pnB9B4ikhmUPR2UJYvI20FZpojcGfEe00Rkloh8FPQaSVD3FREZLyLLROTsYJSp+SLydkQsQ0RkurgR2R6OKH84WG5mUEeC8gwReUJEvgX+KiJdxY3cNkPc6GWph/BvMvHCd18U9rBH5APoAfw7eD4BOBVoAcwJynoBLwTPjwKmB88fAvoDfXF7ypWC8gygE67PlvuDsmq4/lgqBK8nAu2D9/kpKEsK6tQD+kXMmwzUwHWJvQI4DHck/Q1uQJiTgC8jPk/t4G+9iLLHgNuD528Dw3H9xHQFtgWxJOGOfk4I6tWNeP8M4LjI8uD5MOCyiM89OGJaHfae8/sj8Kzv/7U9/D/sCMDEmu64DSLB3+4Fpn8IXCoiFXADj7wdMe0G3BgFV6tqTkT5a7gE8jiAqu7AbbAvFZFjcIkgU1WXAxtFpANwITBDVTcC04DeIvIQ0F5VtwMnAxnqusfe0//9WcAy4AgReTnoIXNbEEO74OglE+iJGyJxj9GqqrgOwtYFsYSBubikBHCtiPwEzAjmbROUnxPs2WfiRmeLXO6IiOdNgXFBvbsL1DMJyhKAiRkiUgs37sCgoC/1e3BdTf/ve6quq+EvcXvL1wLvRSxiDm6D2ZTfmojbUFaOKHsduAnoDbxVRPmbwXt+h9u4rwKGiciNFD64B6q6GTd2dAbwl2B54BJVX1Vtj+tVNTKWPckqHPF8z+uUoBvl/sB56sbcHQNUDj7PYKBbsNyhBZa7I+L5y8DAoN6tBeqZBGUJwMSSq4CRqnq4uv7Um+G6ED6rQL3XgZeAaaoaOR7rDNzGLV1EGkeUvwGMBT6UYPAadYP8NAOuxzUP7TEKN8j3ycA4ABE5HFivqkODZZ0ITAHOFpH64gY57wF8KyL1gSRV/Qh4IKgLrtloTXDk0vMA10tN3MZ8a9B2v2cktj0b8Q0iUp294zIUphYugcHeMQxMgrOrgEwsuQ54tUDZKAo0A6nqjyKyjd/uue+Z9kNwOegYEbkgovy54AhjmIj0DJpYPsC1sW+OqJcrIuNxYx3nB8WdgbtFJA/IBm5U1TUich9uQBwBxqrqpyJyPG4M6T07V/cFfx/AJY1fcE09NaJdKao6S0Rm4JqEluHOjaCqW0RkaLC85bimqqI8hEuAq3CDtreM9v1N/LIbwUy5E+zdZwDHBBvyg13OZ8Dzqvp1RFkS8BNwjaouPtRYjYll1gRkypWg/X0K7qqcg9r4BzdDLQJ2Fdj4t8GNbPW1bfxNIrAjAGOMSVB2BGCMMQnKEoAxxiQoSwDGGJOgLAEYY0yCsgRgjDEJ6v8Bfo3yFAviRT8AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = 50\n", "x_max = 150\n", "\n", "loc = 100\n", "scale = 16\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.030)\n", "plt.xlabel('Älykkyysosamäärä')\n", "\n", "x1 = 80\n", "x2 = 110\n", "r1 = np.linspace(x1, x2, 30)\n", "r2 = norm.pdf(r1, loc, scale)\n", "plt.fill_between(r1, r2, color='C0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yllä lasketun mukaan noin 62,8 % amerikkalaisista on älykkyysosamäärältään välillä 80 - 110.\n", "\n", "Entäpä jos halutaan tietää minkä älykkyysosamäärän ylittää älykkäin kymmenesosa amerikkalaisista? Kysytään siis satunnaismuuttujan arvoa, jonka ylittää 10 % amerikkalaisista eli kysytään satunnaismuuttujan arvoa, jonka alittaa 90 % amerikkalaisista: " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "120.5048250487136" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm.ppf(0.90, loc, scale)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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pOhITAywBmNiyZxtMf8Ub0TKl4MRz5qglV4cz74C0r2HNDNfRGMcsAZjYMvU5yNnr3cFqSkeXm6FKPQg94ToS45glABM7Mrd449Z07AMNjncdTfyqWBW63gUrQ7B6qutojEOWAEzsmPo85O6Hbve5jiT+dR4IVRvYFUEBZwnAxIY9W2HWa9DhKqjfxnU08a9iFTjrDvjlW1gz3XU0xhFLACY2TP2PN/Bbtz+7jiQ4Ov/OPxdgRwFBZQnAuLdnm9f33+FKqN/WdTTBUbGqdxSwcjKsnek6GuOAJQDj3rQXvCt/rO+/7J32e/++ADsKCCJLAMatvdth5jBof7ld+eNCxare3cErvrG7gwPIEoBxa/pL3l2/tvfvzmk3Q+U6dhQQQJYAjDv7dsCMV70xf+yuX3eSq8GZt0HaVzZSaMBYAjDuzHgVsnbZlT+x4LSboVIt+O5friMxZcgSgHFj/y6v+6ftxdCwo+toTKUacMatsHQCbJjnOhpTRiwBGDdmDoP9GdDd9v5jxum3QHINOwoIEEsApuxlZcK0F6H1BdDoFNfRmHyVa3lJYPE4mzs4ICwBmLI3ewTs225X/sSiM26FitXg+3+7jsSUAUsApmxl7/WGfTj2HGh6mutoTEFV6ng3hy34CLYscx2NKWVRJQAR6SkiS0UkTUQOmqZJRJJFZLS/fIaItPDL64rIZBHJFJEXCqwT8rc51380KIkPZGLcj2/Cni3Q3fb+Y9aZt0NSJfj+adeRmFJWbAIQkUTgRaAX0A7oJyIFL9oeCOxQ1VbAUOApv3w/8BBwbxGb76+qJ/uPzUfyAUw5krMfpjwHLc6G5me6jsYUpWo9OG0gzP8Atq90HY0pRdEcAXQB0lR1papmA6OA3gXq9Abe8p+PAXqIiKjqHlX9AS8RmKCbMxIyN9p1/+XBmbdDQhJ8/4zrSEwpSoqiTmNgbcTrdOD0ouqoaq6IZAB1ga3FbPsNEckDPgQeU1UtWEFEBgGDAFJSUgiFQlGEXHoyMzOdxxArDqctJJzD6TOGkFXjeOasDsOa6NYrL+Lxe9Gq4Xk0mvsuM5K7kVUp+h7aeGyLIxXrbRFNApBCygr+UEdTp6D+qrpORKrjJYDfAm8ftBHVYcAwgM6dO2tqamqxAZemUCiE6xhixWG1xY9vQtZWKvV5ldTW55RmWE7E5ffilFbw3Jf8JncapA6NerW4bIsjFOttEU0XUDrQNOJ1E2B9UXVEJAmoCWw/1EZVdZ3/dzfwLl5Xk4lHeTleV0KjU6BVD9fRmGjVbAKn9Ic578Cugv/lTTyIJgHMAlqLSEsRqQj0BcYVqDMOGOA/7wNMKqw7J5+IJIlIPf95BeASYMHhBm/KifkfwM7V3nX/UtjBoolZXe+GcJ538t7EnWITgKrmArcBE4HFwPuqulBEHhWRy/xqI4C6IpIG3AP871JREVkFPAPcKCLp/hVEycBEEZkHzAXWAcNL7mOZmBHOg+/+DSkdoW0v19GYw1W7BZzUz+vC273JdTSmhEVzDgBVnQBMKFD2cMTz/cDVRazboojNdoouRFOuLfgItq+Aa0ba3n95dfY98PO7MPV5uPBx19GYEmR3ApvSE87zBhZr0A6Ov8R1NOZI1T0OOl4Ds1+HzC2uozElyBKAKT2LPoGtS73r/hPsq1audbsXcvZ58zebuGH/K03pCIe9vv96bbwZv0z5Vq81dLgSZr3mzeNs4oIlAFM6lo6HzQv9vf9E19GYktDtz978zdNfch2JKSGWAEzJU4Vvn4I6x0H7K11HY0pKgxO8o7kZr3rzOZtyzxKAKXlLJ8DG+V6/cWJUF5qZ8qLbfd48ztNfdh2JKQGWAEzJUoXQEKjd0rtyxMSXhh3ghEth+iuwb6fraMxRsgRgStayL2DjPK+/2Pb+41P3+yErA2a84joSc5QsAZiSowqhJ727R0+81nU0prQ07Ojd1zHtJTsKKOcsAZiSs2wibPjZ9v6DoPt9/lHAq64jMUfBEoApGarw7RCo1dz2/oPgmJOg7cUw/UXYn+E6GnOELAGYkrH8S1g/x7/yp4LraExZSL3f+/GfbucCyitLAOboqcLkxw+MHGmC4ZiT/HMBL9q5gHLKEoA5eksneH3/3e+3vf+gSR3snQuwu4PLJUsA5uiEwzD5Se+uX7vuP3gadvTuDp72ko0RVA5ZAjBHZ8mnsGm+tydoV/4EU/fB3hhBNlJouWMJwBw59ff+67WBDle5jsa4ktLOGyl0+iuwZ5vraMxhsARgjlj9LVNgy2Kv799G/Ay27vdDzl6Y8qzrSMxhsARgjkxeLi1/eQ/qnwDtr3AdjXGtflvoeDXMHE7FLBsptLywBGCOzLxRVNm3Ds79q+39G0/qYAjn0GzNB64jMVGyBGAOX24WhJ5iV/XWcPzFrqMxsaLucXDK9TRaPxF2rnEdjYmCJQBz+H58CzLW8EvL/iDiOhoTS7rdBwiEnnIdiYmCJQBzeLL3wHf/guZd2VH7ZNfRmFhTszHrGveCn9+FrctdR2OKYQnAHJ6Zw2DPZujxkO39m0KtaXYV4aRKrBrzF9ehmGJYAjDR27cTfngWWl8Azc5wHY2JUTkVa5He9iZabPySNQunuQ7HHIIlABO9Kc96oz+e+5DrSEyMW3fCzezQamR8+qDrUMwhWAIw0dm13rvTs+PVcMyJrqMxMS6vYnWGcwUd9//I8umfuQ7HFCGqBCAiPUVkqYikicjgQpYni8hof/kMEWnhl9cVkckikikiLxRYp5OIzPfXeV7EOpRjWmgIhHPhXNujM9EZLReSrvXgq7+h4TzX4ZhCFJsARCQReBHoBbQD+olIuwLVBgI7VLUVMBTIvwZsP/AQcG8hm34ZGAS09h89j+QDmDKwZRnMGQmn/d4b89+YKGRTkWdy+tA6L41F34x0HY4pRDRHAF2ANFVdqarZwCigd4E6vYG3/OdjgB4iIqq6R1V/wEsE/yMixwA1VHWaqirwNnD50XwQU4omPQoVqnqzfRlzGD4Od2VxuCk1pw4hnJPtOhxTQDTj9zYG1ka8TgdOL6qOquaKSAZQF9h6iG2mF9hm48IqisggvCMFUlJSCIVCUYRcejIzM53HUJZqZCzl1MWf8kuL/qyeteBXy4LWFodibXFAZmYmrJzLH9tmkRdWlu+5hsvWP83P7zzAjpaXug6vTMX69yKaBFBY37weQZ0jqq+qw4BhAJ07d9bU1NRDbLb0hUIhXMdQZlRhxONQLYWW/f5Jy+Rqv1ocqLYohrXFAaFQiKTGHXhg2o/s3p8LnEr9Cu1ou/p92vb5K5Wq13YdYpmJ9e9FNF1A6UDTiNdNgPVF1RGRJKAmcKjpgdL97Rxqm8a1hWMhfaZ32WeBH39joic8ltufWrqbBaP/5joYEyGaBDALaC0iLUWkItAXGFegzjhggP+8DzDJ79svlKpuAHaLyBn+1T83AJ8cdvSm9OTsh68fgZQOcPJ1rqMx5dxCbcnYcFc6rn2XHetsiIhYUWwCUNVc4DZgIrAYeF9VF4rIoyJymV9tBFBXRNKAe4D/XSoqIquAZ4AbRSQ94gqiPwKvAWnACuDzkvlIpkTMfBV2roYLHrPhnk2J+FfONYQRVr1/v+tQjC+qSVxVdQIwoUDZwxHP9wNXF7FuiyLKZwMdog3UlKE92+C7p6H1hXDcOa6jMXFiI3UZlncxd2aMZe3872jasZvrkALP7gQ2Bws96U3yfcE/XEdi4syruZeyWWuxd9z93kUGxilLAObXNi2E2a9D55u8af6MKUF7qcS/cq+hbc4iFn45wnU4gWcJwBygCp/fD5VqwDk25IMpHWPyuvFz+FjqT3uc7L27XIcTaJYAzAGLPoFV33vz/Fap4zoaE6eUBP6ecwMN2M7CUQ8Xv4IpNZYAjCd7L3z5V0jpCJ1uch2NiXM/aRs+zDub9qtHsn3tYtfhBJYlAOOZ8hxkrIVeT9lln6ZMDMnpSzZJrBt9j+tQAssSgIEdq7zJXjpcBS3Och2NCYgt1Ob53CvomDmVFVM/ch1OIFkCCDpVGH8vJCTB+XbZpylbb+T1Ynm4MZW/Gkxe1h7X4QSOJYCgWzwO0r6Cc/4CNQsdkNWYUpNDEg/l3kQj3cSC92yq0bJmCSDIsnbD54O9E79dbnEdjQmo6eF2fJh3Nu1+eZNtv/zsOpxAsQQQZJOfhN0b4NJnITGqUUGMKRVP5FzHHiqxbfRtdodwGbIEEFQb5sGMl707fpt0dh2NCbht1GRIbj/a7J/Hsomvug4nMCwBBFFeLoy7HarUhR52I46JDaPzUpkdbkOD6f9g3/YNrsMJBEsAQTTtP7BhLlz0b6gcnNmZTGxTErg/52aq6H5WvH2r63ACwRJA0Gxd7vX9n3AptL/cdTTG/MoKbcxzuVfSYeckfvl+lOtw4p4lgCAJh+GT26BCZbjoadfRGFOoV/MuYWG4OTW+GUz27kPNLGuOliWAIJk1HNZOh55DoHqK62iMKVQuSdyXcws1NYNlb9/uOpy4ZgkgKLat8Ob4bXUenNTXdTTGHNJCbcEreZfSYctnrJlmw0SUFksAQZCXCx8NgsSKcNl/QMR1RMYU6/ncK1kcbka1iXeRlbHJdThxyRJAEPwwFNbNhkuegRqNXEdjTFSyqcBdObdSTffwyxu/txvESoElgHi37if4dgh0vNob7dOYcmSpNuOfuddy/M7vWPn1cNfhxB1LAPEsey+MvQWqpcBF/3IdjTFHZEReL6bltaPBlIfZs2mF63DiiiWAePbFYNi6DHq/aDd8mXJLSeDenFtQhc1v9Ie8HNchxQ1LAPFq/hj46S3oeg8cd47raIw5Kuuoz/05N9Ny/2KW/vde1+HEDUsA8WjbCvj0Tmh6BpzzoOtojCkRE8JnMDL3PNqufJMNsz52HU5csAQQb3Kz4IMbIbEC9BlhwzybuPJY7vUsCjenyvjb2L9tjetwyj1LAPHmiwdg4zy4/GWo2cR1NMaUqCwq8qecO0jSHDaMuA5ys12HVK5FlQBEpKeILBWRNBEZXMjyZBEZ7S+fISItIpY94JcvFZELI8pXich8EZkrIrNL4sME3k8jYfYIOPMOaNvLdTTGlIpf9BjvfMDe+SwfeYfrcMq1YhOAiCQCLwK9gHZAPxFpV6DaQGCHqrYChgJP+eu2A/oC7YGewEv+9vKdo6onq6rNSHK00n+E8ffAsanQ42+uozGmVH0W/g2v5l5M69XvkT7J7g84UtEcAXQB0lR1papmA6OA3gXq9Abe8p+PAXqIiPjlo1Q1S1V/AdL87ZmStHsTjL4eqh8Dfd6wfn8TCP/M7cv3eR1o8N1gMtKmuw6nXIomATQG1ka8TvfLCq2jqrlABlC3mHUV+FJEfhSRQYcfugH8k74DYN8O6PtfqFLHdUTGlIk8Erk953Y2aW1y3r2O3J3rXYdU7kSzq1jYyGEFB+Uoqs6h1j1LVdeLSAPgKxFZoqrfHfTmXnIYBJCSkkIoFIoi5NKTmZnpPIb/UeX4Jc/ScNM0Fra7ly1LtsGSUJm9fUy1hWPWFgdkZmbCyrn8sW0WeeHSHr+nMj9k3Umftf8g49WLWdj5ScKJlUr5PaMX69+LaBJAOtA04nUToGCqza+TLiJJQE1g+6HWVdX8v5tFZCxe19BBCUBVhwHDADp37qypqalRhFx6QqEQrmP4n8lPwKYQnPtX2nf7c5m/fUy1hWPWFgeEQiGSGnfggWk/snt/bhm847F8lXA7w8NP02zxS7S4dSwkJBa/WhmI9e9FNF1As4DWItJSRCrindQdV6DOOGCA/7wPMElV1S/v618l1BJoDcwUkaoiUh1ARKoCFwALjv7jBMjcd+Hbp+CU6+FsuzPSBNuk8Kn8PfcGWmz9ltXv3uk6nHKj2CMAVc0VkduAiUAi8LqqLhSRR4HZqjoOGAGMFJE0vD3/vv66C0XkfWARkAv8SVXzRCQFGOudJyYJeFdVvyiFzxefVkyGcXd4V/xc8qyN728M8HbehTSTzfw+bSTrP29Bo162Y1ScqC4XUdUJwIQCZQ9HPN8PXF3Euo8DjxcoWwmcdLjBGmDtTBh1HdRrA9e87d3xa4wB4Inc/jSSbVw04x9sqlKLlO6/dx1STLPrBcuTjfPhv69yuGAAABEmSURBVH2gekP47VioVNN1RMbElDAJ3JXzJ6qxj7Mm38u2ytWp2+Va12HFLBsKorzYmgYjr4CK1eGGT2xSd2OKkE0Fbsm5mznh1tSYcCsZ8z93HVLMsgRQHmxdDm9d6k2Jd8PHUKuZ64iMiWn7qMTvsv/M8nBjKn14A7sXTHQdUkyyBBDrNi+BNy6CvGwYMA7qtXYdkTHlwi6q0j/7AVaGjyF5zHXs+vkz1yHFHEsAsWzjAnjzYpAEuGkCpLR3HZEx5coOatA3+0GWhJtReewAMn76yHVIMcUSQKxaOwveugSSkr0f//ptXUdkTLmUQTX6Z/+FBeGWVB03kIzp77gOKWZYAohFS8Z7P/6VasGN46Huca4jMqZc200Vrs8ezKzw8dT84k9s/eJJ75xawFkCiDWzXvNG9mzQDgZ+BXVauo7ImLiwh8oMyL6fT/LOpN70IWwefRuE81yH5ZQlgFiRlwsTH4Tx/wetL4AbP4Nq9V1HZUxcyaYCd+Xcyiu5l9JgyTtsHn4l7N/lOixnLAHEgr3bvRu8pr0Ap/0erv0vVKzqOipj4pKSwJDcfvw15ybqrP+Obc+djW5Z5josJywBuLZpIQw/B1ZPgUufh4uftgldjCkD7+Sdz/U5f0H2bmPfS93ZvyB4l4laAnBFFX58E4b3gJz9cOME6DSg2NWMMSVnergdl2Q9zspwCpXG9GfHJ4MDNdG8JQAX9u2A92+AT++EZqfDLd9C09NcR2VMIK2nHldl/Y138npQe87LbP9PKro1zXVYZcISQFlbMRle7gpLJ8D5j8L1Y73B3YwxzmRRkb/mDOSW7LtI2LmKrBe7sn/6iLi/VNQSQFnZtwM++ROMvBwqVIKBX8JZd0KC/RMYEysmhrvQK2sIc/OOpdIX97DjlV6w/RfXYZUa+/Upbaqw8GN48XSY+x50vRv+MAUad3IdmTGmEBuoS7/sB3ggZyAVNs4l+z+ns+/bZyEvx3VoJc4SQGnauMAbxfODAVCtAdw8Cc57xDsCMMbELCWB9/J6cF7WP/k+rwOVJ/+NXUNPI7zsK9ehlShLAKVh90b47G549WzYtMC7tPPmEDQ62XVkxpjDsJG6DMy+h99l38uO3ftIeLcPGSOuhE2LXIdWIuyC85K0ZytMeRZmDvcOF0+7GVIHQ5U6riMzxhwxYVL4VH7I6siAxIncuWYs4ZfPZG+by6l2wV+hXivXAR4xSwAlIWMdzHgZZr0OufvgxGuh+31Q51jXkRljSkg2FRiedwkf5HXnD0njuWHpBPKWfULWCVdSpfvd0LCD6xAPmyWAo7FxPkx9ARaMAQ1D+yug+/02dLMxcWwn1RmS25fXcntxa4VPuXbRp7B4DJlNu1Mt9S5omVpuru6zBHCYEvKyYM473l286bOgQlVv/J4zboXazV2HZ4wpI1upyaM51/Mcl/PbpK8ZsGYi1UZewd5qzal0xkASTunvOsRiWQKIRjgPVn0P8z/gzHkfQd5eqNcGLnwSTuprffzGBFgG1Xgh93KG515Er4SZ/Hb3JDp9/TB53zxKuzqdoP5OaHMhVKjsOtSDWAIoSm42rP4Bln4Oi8ZB5kaoWI2t9U6nYa8/Q/MzQcR1lMaYGJFFRT4Od+XjrK60lnT6V5jM1TunwgcDyEmqira5iIrtL4FWPSC5uutwAUsAv7ZjNawMwYpJ3iNrFyRV9v7BOvaBNj1ZMmUGDVuc5TpSY0wMW65NeCT7t2S2uZapi5bRR6dyzsLPqbjoA/KkAjnNulKp7Xlw3Dne5E+OdiaDmwDCYdi2HNZMh7UzveGYd/i3fFc/BtpfDm0vgpbdoWIVt7EaY8ollQSmhjswNasDiQykkyyjZ4WfSF01h2NXTwYgq1I9ElucRVKL30DTLtDwREisUCbxBSMB5GZ7P/abF8OGubB+LmyYB1kZ3vLKdaDZb+CMP8KxqV7/vnXvGGNKUB6JzNQTmJl9Ao/Sn4Zs46zEhaTqQk5ZPIUmSz7x6iUkk1u/PRWbnoo0OhlS2kH940tlkqj4SQB5OZCRDhlrYftK2LbC+7t1OWxfAeFcr15iMqS0hw5XeuPxNDsD6rayH3xjTJnaSF0+zOvGh3ndAGjINjolLKdLhRWcsHEl7Tb+l2ry2v/qZ1dvSmKDtiTWawV1jvPuM6rVDGo1PeITzFElABHpCTwHJAKvqeqQAsuTgbeBTsA24FpVXeUvewAYCOQBd6jqxGi2Waj9GfDT27BnC+zeBLvXe8Mu7FoPuzd41+LnS6wItVt6P+4nXAoNTvCyaP22ZXZ4ZYwx0dpIXcaH6zI+6wwAhDDNZDNtZS3tk9bRZlc6zTKW03LF91Qh61fr5lSqBzUakVSrEVKjEVRr6M0pXtV/FKHYBCAiicCLwPlAOjBLRMapauRgGAOBHaraSkT6Ak8B14pIO6Av0B5oBHwtIm38dYrb5sG2r4Rxt3vPk2t4ffXVG0LLblCz6YFsWLsl1GwCCYnFfTxjjIlJSgKrtSGrtSFfZp/2qyX12UkL2UTTxK00T9xG4/1bqL93Ow02LiIlYQp12P2rbUlScqEjUEZzBNAFSFPVlQAiMgroDUT+WPcGHvGfjwFeEBHxy0epahbwi4ik+dsjim0erH5buGsiVK0Xk9fUGmMO0DifTMUdYQu12aK1mZUL5B5cowK51GY39SSDepJBQuWhhd6sFE0CaAysjXidDpxeVB1VzRWRDKCuXz69wLqN/efFbRMAERkEDPJfZkrtZkujiLk01QO2Oo4hVlhbHGBtcUA9qZC8J6l24zZAoE+u3b1vlyRUruEkE66OeJ63N6PQGw+iSQCF/QMW/EBF1SmqvLCBMgptJFUdBgw7VIBlSURmq2pn13HEAmuLA6wtDhCR2eHs/dYWeG2Ru2tLzLZFNCMWpQNNI143AdYXVUdEkoCawPZDrBvNNo0xxpSiaBLALKC1iLQUkYp4J3XHFagzDhjgP+8DTFKvA3Ac0FdEkkWkJdAamBnlNo0xxpSiYruA/D7924CJeJdsvq6qC0XkUWC2qo4DRgAj/ZO82/F+0PHrvY93cjcX+JOq5gEUts2S/3ilIma6o2KAtcUB1hYHWFscENNtIXam3hhjgql8zFpgjDGmxFkCMMaYgLIEUAwRqSUiY0RkiYgsFpHfiEgdEflKRJb7f2u7jrMsiMjdIrJQRBaIyHsiUsk/kT/Db4vR/kn9uCMir4vIZhFZEFFW6PdAPM+LSJqIzBORU91FXvKKaIt/+f9H5onIWBGpFbHsAb8tlorIhW6iLh2FtUXEsntFREWknv865r4XlgCK9xzwhaoeD5wELAYGA9+oamvgG/91XBORxsAdQGdV7YB38j5/2I+hflvswBsWJB69CfQsUFbU96AX3hVvrfFuYny5jGIsK29ycFt8BXRQ1ROBZcADAAWGg+kJvOQPLxMv3uTgtkBEmuINdbMmojjmvheWAA5BRGoA3fCuckJVs1V1J96wFW/51d4CLncTYZlLAir793pUATYA5+IN/wFx3Baq+h3eFW6Rivoe9AbeVs90oJaIHFM2kZa+wtpCVb9U1fxBCabj3dsDEcPBqOovQORwMOVeEd8LgKHAffz6BteY+15YAji0Y4EtwBsiMkdEXhORqkCKqm4A8P82cBlkWVDVdcC/8fZoNgAZwI/Azoj/+JFDfQRBUd+DwoZPCVK7/A743H8euLYQkcuAdar6c4FFMdcWlgAOLQk4FXhZVU8B9hCA7p7C+P3bvYGWeCO7VsU7pC3IriuObviUuCQiD+Ld8/Pf/KJCqsVtW4hIFeBB4OHCFhdS5rQtLAEcWjqQrqoz/Ndj8BLCpvxDN//vZkfxlaXzgF9UdYuq5gAfAWfiHcbm31AYtCE9ivoeBHKoExEZAFwC9NcDNxgFrS2Ow9tJ+llEVuF93p9EpCEx2BaWAA5BVTcCa0WkrV/UA++u5sihLwYAnzgIr6ytAc4QkSr+UN/5bTEZb/gPCE5b5CvqezAOuMG/6uMMICO/qyhe+RM83Q9cpqp7IxYVNRxMXFLV+araQFVbqGoLvB/9U/3fktj7XqiqPQ7xAE4GZgPzgI+B2nhDXX8DLPf/1nEdZxm1xd+BJcACYCSQjHeeZCbeyb0PgGTXcZbSZ38P79xHDt5/6oFFfQ/wDvVfBFYA8/GunHL+GUq5LdLw+rfn+o9XIuo/6LfFUqCX6/hLuy0KLF8F1IvV74UNBWGMMQFlXUDGGBNQlgCMMSagLAEYY0xAWQIwxpiAsgRgjDEBZQnAxBwRmeqPwjrBdSzGxDO7DNQYYwLKjgBMzBGRK/xx1Dv5r1sUNt56gXUeEZF7CykPiUjn0oq1rIjIZSIyWERuEJE/RJR39seYP8+fp/tQ27AjK/MrxU4Kb4wDfYEfgGvxRhwNPFUdhzeUQMHy2Xh3qgN8Xdi6IpKkqrmqeqZfdFHpRGnKGzsCMDHFH267O97wAlf74w5FLv9eRE6OeD1FRE4sUOdmEflcRCpHlCWIyFsi8piIDBSRoQXqPyMi/xCROyPKHxeRO0TkGBH5TkTmijcb2tn+8n4iMt8ve8ovSxSRN/2y+SJyd8R7zBKRn0XkQ3/USPy6L4vIZBFZKSLd/VmmFovImxGxDBOR2eLNyPb3iPK/+9ud79cRvzwkIk+IyLfAnSLSW7yZ2+aIN3tZylH8M5l44XosCnvYI/IB9APe8Z9PAX4DtAAW+GUDgGf9522A2f7zR4B7gdvw9pST/fIQcAbemC0P+mVV8cZjqeC/ngp09N/nJ78swa9TF/i/iHUTgep4Q2KvAerjHUlPwpsQphPwVcTnqeX/rRtR9hhwu//8TWAU3jgxvYFdfiwJeEc/J/v16kS8fwg4MbLcfz4SuDTic78Usaw2B875/R542vW/tT3cP+wIwMSavng/iPh/+xZY/gFwiYhUwJt45M2IZb/Fm6PgKlXNiih/FS+BPA6gqnvwfrAvEZHj8RLBfFVdBWwTkVOAC4A5qroNmAXcJCKPAB1VdTdwGhBSb3js/PHvuwErgWNF5D/+CJm7/Bg6+Ecv84H+eFMk5vtUVRVvgLBNfixhYCFeUgK4RkR+Aub467bzy8/x9+zn483OFrnd0RHPmwAT/Xp/LlDPBJQlABMzRKQm3rwDL/pjqd+HN9T0/76n6g01/BXe3vI1wLsRm1iA94PZhF+bivdDWSmi7DXgRuAm4I0iyl/33/M7vB/3dcBIEbmBwif3QFV34M0dHQL+5G8PvER1m6p2xBtVNTKW/GQVjnie/zrJH0b5XqCHenPujgcq+Z/nJaCPv93hBba7J+L5f4AX/Hq3FKhnAsoSgIklVwJjVLW5euOpN8UbQrhbgXqvAc8Ds1Q1cj7WOXg/buNEpFFE+QhgAvCB+JPXqDfJT1PgOrzuoXxj8Sb5Pg2YCCAizYHNqjrc39apwAygu4jUE2+S837AtyJSD0hQ1Q+Bh/y64HUbbfCPXPofZrvUwPsxz/D77vNnYsv/Ed8qItU4MC9DYWriJTA4MIeBCTi7CsjEkmuBVwqUjaVAN5Cq/igiu/j1nnv+sh/8y0HHi8j5EeXP+EcYI0Wkv9/F8j5eH/uOiHrZIjIZb67jPL84FfiziOQAmcANqrpBRB7AmxBHgAmq+omInIQ3h3T+ztUD/t+H8JLGaryunurRNoqq/iwic/C6hFbinRtBVXeKyHB/e6vwuqqK8gheAlyHN2l7y2jf38QvuxHMlDv+3n0ION7/IT/S7XwGDFXVbyLKEoCfgKtVdfnRxmpMLLMuIFOu+P3vM/CuyjmiH3//ZqhlwL4CP/7t8Ga2+sZ+/E0Q2BGAMcYElB0BGGNMQFkCMMaYgLIEYIwxAWUJwBhjAsoSgDHGBNT/Awdig3TebZqeAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = 50\n", "x_max = 150\n", "\n", "loc = 100\n", "scale = 16\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.030)\n", "plt.xlabel('Älykkyysosamäärä')\n", "\n", "x1 = 120.5\n", "x2 = 150\n", "r1 = np.linspace(x1, x2, 30)\n", "r2 = norm.pdf(r1, loc, scale)\n", "plt.fill_between(r1, r2, color='C0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yllä lasketun mukaan kyseinen älykkyysosamäärä on noin 120,5.\n", "\n", "Esimerkki. Oletetaan, että aikaisemmista myyntitilastoista voidaan todeta, että päivittäistavaran kysynnällä lauantaisin on ollut keskiarvo 120 ja keskihajonta 15. Kauppias voi käyttää normaalijakaumaa määrittäessään seuraavan lauantain tilausmäärää kyseisen päivittäistavaran kohdalla. Oletetaan, että kauppias haluaa 95 % varmuuden tavaran riittävyydelle:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "144.67280440427209" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q = 0.95\n", "loc = 120\n", "scale = 15\n", "\n", "norm.ppf(q, loc, scale)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = 70\n", "x_max = 170\n", "\n", "loc = 120\n", "scale = 15\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.030)\n", "plt.xlabel('Kysyntä')\n", "\n", "x1 = 70\n", "x2 = 145\n", "r1 = np.linspace(x1, x2, 30)\n", "r2 = norm.pdf(r1, loc, scale)\n", "plt.fill_between(r1, r2, color='C0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pitää siis tilata tavaraa 145 kpl.\n", "\n", "Esimerkki. Paperikone voidaan säätää valmistamaan eri painoisia paperilaatuja (80 grammaa/neliömetri, 85 grammaa/neliömetri jne.). Teollisesti valmistetun tuotteen ominaisuudet kuitenkin vaihtelevat monien satunnaisten tekijöiden takia. Vaikka kone on säädetty valmistamaan 80 g paperia, niin paperi ei ole kauttaaltaan 80 g. Oletetaan, että paperin tilaaja vaatii, että 90 % paperista täytyy olla yli 80 g. Minkälaista paperia paperikone pitäisi säätää valmistamaan (oletus: paperin neliömetripainon odotusarvo on säädettävissä). Oletetaan, että valmistusprosessiin ja kyseiseen paperikoneeseen liittyvä keskihajonta on 2,5 grammaa/neliömetri." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "80.00612108613849" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q = 0.10 #haetaan rajaa, jonka alapuolelle jää 10 %\n", "loc = 83.21 # tähän löydetään sopiva arvo kokeilemalla\n", "scale = 2.5\n", "\n", "norm.ppf(q, loc, scale)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = 70\n", "x_max = 96\n", "\n", "loc = 83.21\n", "scale = 2.5\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.20)\n", "plt.xlabel('Paperin neliömetripaino')\n", "\n", "x1 = 80\n", "x2 = 96\n", "r1 = np.linspace(x1, x2, 30)\n", "r2 = norm.pdf(r1, loc, scale)\n", "plt.fill_between(r1, r2, color='C0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Kokeilemalla odotusarvon loc kohdalle erilaisia arvoja, selviää että säädettäessä odotusarvo 83,21 gramman kohdalle, 90 % paperista on yli 80 grammaista.\n", "\n", "Edellä olleista esimerkeistä nähdään normaalijakauman soveltuvan malliksi hyvin erilaisiin käytännön tilanteisiin. Yhteistä edellä tarkastelluille satunnaismuuttujille on, että niiden arvoihin vaikuttavat monet satunnaiset tekijät. Tämä pätee yleisemminkin: \n", "\n", "jos satunnaismuuttujan arvo määräytyy satunnaisesti lukuisten eri tekijöiden vaikutuksesta, niin muuttuja yleensä noudattaa likimain normaalijakaumaa.\n", "\n", "Joitain kaikille normaalijakaumille päteviä todennäköisyyksiä on hyvä pitää mielessä:\n", "
    \n", "
  • Todennäköisyys saada jotain väliltä odotusarvo +/- keskihajonta on noin 68 %
  • \n", "
  • Todennäköisyys saada jotain väliltä odotusarvo +/- 2 keskihajontaa on noin 95 %
  • \n", "
\n", "Huomaa, että yllä oleva pitää paikkansa riippumatta odotusarvosta ja keskiarvosta! Tarkistetaan vielä laskemalla yllä mainitut todennäköisyydet älykkyysosamäärän normaalijakaumalle:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.6826894921370859\n", "0.9544997361036416\n" ] } ], "source": [ "loc = 100\n", "scale = 16\n", "\n", "print(norm.cdf(loc + scale, loc, scale) - norm.cdf(loc - scale, loc, scale))\n", "print(norm.cdf(loc + 2*scale, loc, scale) - norm.cdf(loc - 2*scale, loc, scale))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = 50\n", "x_max = 150\n", "\n", "loc = 100\n", "scale = 16\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.030)\n", "plt.title('Kahden keskihajonnan päässä odotusarvosta noin 95 %')\n", "plt.xlabel('Älykkyysosamäärä')\n", "\n", "x1 = 68\n", "x2 = 132\n", "r1 = np.linspace(x1, x2, 30)\n", "r2 = norm.pdf(r1, loc, scale)\n", "plt.fill_between(r1, r2, color='C0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Standardi normaalijauma

\n", " \n", "Standardoitu satunnaismuuttuja eli standardipiste tarkoittaa satunnaismuuttujaa, jonka arvot on muunnettu standardia normaalijakaumaa vastaaviksi. Standardin normaalijakauman odotusarvo on 0 ja keskihajonta 1 (N(0, 1)). Satunnaismuuttujan standardoinnissa on olennaista todennäköisyyksien säilyttäminen samoina. Edellä jo todettiin, että todennäköisyydet säilyvät kunhan pysytään yhtä monen keskihajonnan päästä keskiarvosta.\n", "\n", "Esimerkki. Jakauman N(120, 20) satunnaismuuttujan 100 standardoitu arvo on noin -1, koska 100 on yhden keskihajonnan verran odotusarvon vasemmalla puolella.\n", "\n", "Yleinen kaava satunnaismuuttujan standardoinnille on: vähennä odotusarvo ja jaa kesihajonnalla.\n", "\n", "Satunnaismuuttujan standardointia käytetään monissa tilastollisissa analyyseissä, mutta myös haluttaessa saada erilaisilla asteikoilla mitatut muuttujat vertailukelpoisiksi keskenään.\n", "\n", "Standardipisteistä nähdään nopeasti esimerkiksi poikkeavat arvot. Esimerkiksi kaikki standardipistettä -2 pienemmät ja standardipistettä 2 suuremmat ovat melko harvinaisia, koska todennäköisyys näin äärimmäisille arvoille on alle 5 %." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_min = -4\n", "x_max = 4\n", "\n", "loc = 0\n", "scale = 1\n", "\n", "x = np.linspace(x_min, x_max, 100)\n", "y = norm.pdf(x, loc, scale)\n", "\n", "plt.plot(x, y, color='C1')\n", "plt.grid()\n", "plt.xlim(x_min, x_max)\n", "plt.ylim(0, 0.40)\n", "plt.title('Kahden keskihajonnan päässä odotusarvosta noin 95 %')\n", "plt.xlabel('Standardipisteet')\n", "\n", "x1 = -2\n", "x2 = 2\n", "r1 = np.linspace(x1, x2, 30)\n", "r2 = norm.pdf(r1, loc, scale)\n", "plt.fill_between(r1, r2, color='C0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Seuraavassa esimerkki standardipisteiden laskennasta:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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nrosukupikäperhekoulutuspalveluvpalkkajohtotyötovtyöymppalkkattyötehttyötervlomaosakuntosahieroja
0113811.022.0358733.0333NaNNaNNaNNaN
1212922.010.0296315.0213NaNNaNNaNNaN
2313011.07.0198934.01131.0NaNNaNNaN
3413621.014.0214433.03331.0NaNNaNNaN
4512412.04.0218323.02121.0NaNNaNNaN
...................................................
777812213.00.0159844.0434NaN1.01.0NaN
787913311.02.0163813.02121.0NaNNaNNaN
798012712.07.0261234.03331.0NaN1.0NaN
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818223523.015.0218334.04341.0NaNNaNNaN
\n", "

82 rows × 16 columns

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" ], "text/plain": [ " nro sukup ikä perhe koulutus palveluv palkka johto työtov työymp \\\n", "0 1 1 38 1 1.0 22.0 3587 3 3.0 3 \n", "1 2 1 29 2 2.0 10.0 2963 1 5.0 2 \n", "2 3 1 30 1 1.0 7.0 1989 3 4.0 1 \n", "3 4 1 36 2 1.0 14.0 2144 3 3.0 3 \n", "4 5 1 24 1 2.0 4.0 2183 2 3.0 2 \n", ".. ... ... ... ... ... ... ... ... ... ... \n", "77 78 1 22 1 3.0 0.0 1598 4 4.0 4 \n", "78 79 1 33 1 1.0 2.0 1638 1 3.0 2 \n", "79 80 1 27 1 2.0 7.0 2612 3 4.0 3 \n", "80 81 1 35 2 2.0 16.0 2808 3 4.0 3 \n", "81 82 2 35 2 3.0 15.0 2183 3 4.0 4 \n", "\n", " palkkat työteht työterv lomaosa kuntosa hieroja \n", "0 3 3 NaN NaN NaN NaN \n", "1 1 3 NaN NaN NaN NaN \n", "2 1 3 1.0 NaN NaN NaN \n", "3 3 3 1.0 NaN NaN NaN \n", "4 1 2 1.0 NaN NaN NaN \n", ".. ... ... ... ... ... ... \n", "77 3 4 NaN 1.0 1.0 NaN \n", "78 1 2 1.0 NaN NaN NaN \n", "79 3 3 1.0 NaN 1.0 NaN \n", "80 3 3 NaN NaN NaN NaN \n", "81 3 4 1.0 NaN NaN NaN \n", "\n", "[82 rows x 16 columns]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Datan avaus\n", "df = pd.read_excel('https://taanila.fi/data1.xlsx')\n", "df" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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nrosukupikäperhekoulutuspalveluvpalkkajohtotyötovtyöymppalkkattyötehttyötervlomaosakuntosahierojapalkka_s
0113811.022.0358733.0333NaNNaNNaNNaN1.204594
1212922.010.0296315.0213NaNNaNNaNNaN0.469914
2313011.07.0198934.01131.0NaNNaNNaN-0.676844
3413621.014.0214433.03331.0NaNNaNNaN-0.494352
4512412.04.0218323.02121.0NaNNaNNaN-0.448435
......................................................
777812213.00.0159844.0434NaN1.01.0NaN-1.137196
787913311.02.0163813.02121.0NaNNaNNaN-1.090102
798012712.07.0261234.03331.0NaN1.0NaN0.056657
808113522.016.0280834.0333NaNNaNNaNNaN0.287422
818223523.015.0218334.04341.0NaNNaNNaN-0.448435
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82 rows × 17 columns

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" ], "text/plain": [ " nro sukup ikä perhe koulutus palveluv palkka johto työtov työymp \\\n", "0 1 1 38 1 1.0 22.0 3587 3 3.0 3 \n", "1 2 1 29 2 2.0 10.0 2963 1 5.0 2 \n", "2 3 1 30 1 1.0 7.0 1989 3 4.0 1 \n", "3 4 1 36 2 1.0 14.0 2144 3 3.0 3 \n", "4 5 1 24 1 2.0 4.0 2183 2 3.0 2 \n", ".. ... ... ... ... ... ... ... ... ... ... \n", "77 78 1 22 1 3.0 0.0 1598 4 4.0 4 \n", "78 79 1 33 1 1.0 2.0 1638 1 3.0 2 \n", "79 80 1 27 1 2.0 7.0 2612 3 4.0 3 \n", "80 81 1 35 2 2.0 16.0 2808 3 4.0 3 \n", "81 82 2 35 2 3.0 15.0 2183 3 4.0 4 \n", "\n", " palkkat työteht työterv lomaosa kuntosa hieroja palkka_s \n", "0 3 3 NaN NaN NaN NaN 1.204594 \n", "1 1 3 NaN NaN NaN NaN 0.469914 \n", "2 1 3 1.0 NaN NaN NaN -0.676844 \n", "3 3 3 1.0 NaN NaN NaN -0.494352 \n", "4 1 2 1.0 NaN NaN NaN -0.448435 \n", ".. ... ... ... ... ... ... ... \n", "77 3 4 NaN 1.0 1.0 NaN -1.137196 \n", "78 1 2 1.0 NaN NaN NaN -1.090102 \n", "79 3 3 1.0 NaN 1.0 NaN 0.056657 \n", "80 3 3 NaN NaN NaN NaN 0.287422 \n", "81 3 4 1.0 NaN NaN NaN -0.448435 \n", "\n", "[82 rows x 17 columns]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Lasketaan palkan standardipisteet uuteen muuttujaan\n", "df['palkka_s'] = (df['palkka'] - df['palkka'].mean()) / df['palkka'].std()\n", "\n", "# Nyt datassa on palkan standardipisteet sarakkeessa 'palkka_s'\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lisätietoa: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }