{"id":5861,"date":"2025-07-03T21:02:54","date_gmt":"2025-07-03T13:02:54","guid":{"rendered":"https:\/\/infernews.com\/?page_id=5861"},"modified":"2025-07-04T21:04:44","modified_gmt":"2025-07-04T13:04:44","slug":"montecarlo","status":"publish","type":"page","link":"https:\/\/infernews.com\/blog\/montecarlo\/","title":{"rendered":"\u8499\u7279\u5361\u7f85\u6a21\u64ec\uff08Monte Carlo Simulation\uff09"},"content":{"rendered":"\n<figure class=\"wp-block-video\"><video height=\"720\" style=\"aspect-ratio: 1280 \/ 720;\" width=\"1280\" autoplay loop muted src=\"\/blog\/wp-content\/uploads\/2025\/07\/Monte_carlo_simulation_202507040046_9b0tw.mp4\"><\/video><\/figure>\n\n\n\n<p>\u8499\u7279\u5361\u7f85\u6a21\u64ec\uff08Monte Carlo Simulation\uff09\u662f\u4e00\u7a2e\u57fa\u65bc\u96a8\u6a5f\u62bd\u6a23\u7684\u8a08\u7b97\u65b9\u6cd5\uff0c\u7528\u65bc\u6a21\u64ec\u548c\u5206\u6790\u8907\u96dc\u7cfb\u7d71\u6216\u904e\u7a0b\u4e2d\u7684\u4e0d\u78ba\u5b9a\u6027\u3002\u5b83\u901a\u904e\u591a\u6b21\u96a8\u6a5f\u8a66\u9a57\u4f86\u4f30\u8a08\u7d50\u679c\u7684\u6982\u7387\u5206\u5e03\uff0c\u5ee3\u6cdb\u61c9\u7528\u65bc\u91d1\u878d\u3001\u5de5\u7a0b\u3001\u7269\u7406\u3001\u7d71\u8a08\u7b49\u9818\u57df\u3002<\/p>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"Monte Carlo Simulation\" style=\"width:853px;max-width:100%;margin:5px auto;\"><div class=\"lyMe\" id=\"WYL_7ESK5SaP-bc\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\"><div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F7ESK5SaP-bc%2Fhqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/7ESK5SaP-bc\" \/><meta itemprop=\"duration\" content=\"PT10M6S\" \/><meta itemprop=\"uploadDate\" content=\"2020-09-08T14:55:17Z\" \/><\/div><meta itemprop=\"accessibilityFeature\" content=\"captions\" \/><div id=\"lyte_7ESK5SaP-bc\" data-src=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F7ESK5SaP-bc%2Fhqdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Monte Carlo Simulation<\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/7ESK5SaP-bc\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F7ESK5SaP-bc%2F0.jpg\" alt=\"Monte Carlo Simulation\" width=\"853\" height=\"460\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"A Monte Carlo simulation is a randomly evolving simulation. In this video, I explain how this can be useful, with two fun examples of Monte Carlo simulations: The first model shows how pi can be determined with Monte Carlo sampling, and in the second part of the video we will take a look how animations can be rendered with Monte Carlo path tracing. If you want to see another Monte Carlo simulation in action, check out this video: https:\/\/youtu.be\/PPWEmjnqsF8 If you want to support my channel, subscribing, liking and sharing is an amazing help. Thank you! :) If you feel like this video added value to your life and you want to support MarbleScience even more, please consider becoming a patron. https:\/\/www.patreon.com\/MarbleScience Chapters: 00:00 What are Monte Carlo simulations? 01:01 determine pi with Monte Carlo 03:01 analogy to study design 04:56 back to Monte Carlo 05:57 Monte Carlo path tracing 08:51 summary There is also a text version of this video on my website: https:\/\/marblescience.com\/blog\/monte-carlo-simulations\/ You can also find me at: https:\/\/www.instagram.com\/marblescience\/\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:853px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<h3 class=\"wp-block-heading\">\u6838\u5fc3\u6982\u5ff5<\/h3>\n\n\n\n<ol 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class=\"wp-block-list\">\n<li>\u5b9a\u7fa9\u554f\u984c\u548c\u6a21\u578b\uff1a\u78ba\u5b9a\u9700\u8981\u6a21\u64ec\u7684\u7cfb\u7d71\uff0c\u660e\u78ba\u8f38\u5165\u8b8a\u91cf\uff08\u5982\u6210\u672c\u3001\u6642\u9593\u3001\u5229\u7387\u7b49\uff09\u53ca\u5176\u6982\u7387\u5206\u5e03\u3002<\/li>\n\n\n\n<li>\u751f\u6210\u96a8\u6a5f\u8f38\u5165\uff1a\u6839\u64da\u8b8a\u91cf\u7684\u6982\u7387\u5206\u5e03\uff08\u5982\u5e38\u614b\u5206\u5e03\u3001\u5747\u52fb\u5206\u5e03\u7b49\uff09\uff0c\u96a8\u6a5f\u751f\u6210\u8f38\u5165\u503c\u3002<\/li>\n\n\n\n<li>\u8a08\u7b97\u7d50\u679c\uff1a\u5c07\u96a8\u6a5f\u8f38\u5165\u4ee3\u5165\u6a21\u578b\uff0c\u8a08\u7b97\u6bcf\u6b21\u8a66\u9a57\u7684\u8f38\u51fa\u3002<\/li>\n\n\n\n<li>\u91cd\u8907\u8a66\u9a57\uff1a\u9032\u884c\u5927\u91cf\u8a66\u9a57\uff0c\u6536\u96c6\u6bcf\u6b21\u7684\u7d50\u679c\u3002<\/li>\n\n\n\n<li>\u5206\u6790\u7d50\u679c\uff1a\u5c0d\u6240\u6709\u8a66\u9a57\u7d50\u679c\u9032\u884c\u7d71\u8a08\u5206\u6790\uff0c\u5f97\u51fa\u6982\u7387\u5206\u5e03\u3001\u5e73\u5747\u503c\u3001\u98a8\u96aa\u7b49\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u61c9\u7528\u7bc4\u4f8b<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u91d1\u878d<\/strong>\uff1a\u8a55\u4f30\u6295\u8cc7\u7d44\u5408\u98a8\u96aa\u3001\u9810\u6e2c\u80a1\u50f9\u6ce2\u52d5\u6216\u5b9a\u50f9\u884d\u751f\u54c1\uff08\u5982\u671f\u6b0a\uff09\u3002<\/li>\n\n\n\n<li><strong>\u5de5\u7a0b<\/strong>\uff1a\u5206\u6790\u7d50\u69cb\u53ef\u9760\u6027\u548c\u6545\u969c\u6982\u7387\u3002<\/li>\n\n\n\n<li><strong>\u9805\u76ee\u7ba1\u7406<\/strong>\uff1a\u4f30\u8a08\u9805\u76ee\u5b8c\u6210\u6642\u9593\u6216\u6210\u672c\uff0c\u8003\u616e\u4e0d\u78ba\u5b9a\u56e0\u7d20\u3002<\/li>\n\n\n\n<li><strong>\u7269\u7406<\/strong>\uff1a\u6a21\u64ec\u7c92\u5b50\u904b\u52d5\u6216\u91cf\u5b50\u7cfb\u7d71\u884c\u70ba\u3002<\/li>\n<\/ol>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"A Simple Solution for Really Hard Problems: Monte Carlo Simulation\" style=\"width:853px;max-width:100%;margin:5px auto;\"><div class=\"lyMe\" id=\"WYL_slbZ-SLpIgg\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\"><div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FslbZ-SLpIgg%2Fhqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/slbZ-SLpIgg\" \/><meta itemprop=\"duration\" content=\"PT5M58S\" \/><meta itemprop=\"uploadDate\" content=\"2023-10-12T20:48:21Z\" \/><\/div><meta itemprop=\"accessibilityFeature\" content=\"captions\" \/><div id=\"lyte_slbZ-SLpIgg\" data-src=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FslbZ-SLpIgg%2Fhqdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">A Simple Solution for Really Hard Problems: Monte Carlo Simulation<\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/slbZ-SLpIgg\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FslbZ-SLpIgg%2F0.jpg\" alt=\"A Simple Solution for Really Hard Problems: Monte Carlo Simulation\" width=\"853\" height=\"460\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Today&#039;s video provides a conceptual overview of Monte Carlo simulation, a powerful, intuitive method to solve challenging probability questions. And we get to see how we can use it to answer a realistic question in Python! 0:00 Monte Carlo Applications 0:22 Party Problem: What is The Chance You&#039;ll Make It? 1:16 Monte Carlo Conceptual Overview 3:00 Monte Carlo Simulation in Python: NumPy and matplotlib 5:02 Party Problem: What Should You Do? You can access the dataset and Jupyter Notebook used to run these scripts, which includes proper commenting, at: https:\/\/github.com\/RiskByNumbers\/Monte-Carlo-Simulation-Video. #montecarlosimulation #probability #datascience #python #numpy #tutorial #sampling ===================== Hello, and welcome to RiskByNumbers! I am a professor sharing educational resources around probability, statistics, optimization methods, algorithms, and programming to a broad audience. Outside of Youtube, you can currently find me in Vancouver, Canada at the University of British Columbia. Thank you, and I look forward to seeing you in future videos! Email: RiskByNumbers@gmail.com. LinkedIn: https:\/\/www.linkedin.com\/in\/omar-swei\/\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:853px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<h3 class=\"wp-block-heading\">\u7c21\u55ae\u4f8b\u5b50<\/h3>\n\n\n\n<p>\u5047\u8a2d\u4f60\u60f3\u4f30\u8a08\u4e00\u500b\u9805\u76ee\u7684\u5b8c\u6210\u6642\u9593\uff0c\u5047\u8a2d\u6709\u4e09\u500b\u4efb\u52d9\uff0c\u6bcf\u500b\u4efb\u52d9\u7684\u5b8c\u6210\u6642\u9593\u670d\u5f9e\u67d0\u500b\u6982\u7387\u5206\u5e03\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4efb\u52d9A\uff1a5\u81f37\u5929\uff08\u5747\u52fb\u5206\u5e03\uff09<\/li>\n\n\n\n<li>\u4efb\u52d9B\uff1a3\u81f35\u5929\uff08\u5747\u52fb\u5206\u5e03\uff09<\/li>\n\n\n\n<li>\u4efb\u52d9C\uff1a2\u81f34\u5929\uff08\u5747\u52fb\u5206\u5e03\uff09<\/li>\n<\/ul>\n\n\n\n<p>\u8499\u7279\u5361\u7f85\u6a21\u64ec\u6703\uff1a<\/p>\n\n\n\n<ol 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class=\"wp-block-heading\">\u7e3d\u7d50<\/h3>\n\n\n\n<p>\u8499\u7279\u5361\u7f85\u6a21\u64ec\u662f\u4e00\u7a2e\u5f37\u5927\u7684\u5de5\u5177\uff0c\u7528\u65bc\u5728\u4e0d\u78ba\u5b9a\u6027\u4e0b\u9032\u884c\u6c7a\u7b56\u5206\u6790\u3002\u5b83\u901a\u904e\u6a21\u64ec\u5927\u91cf\u96a8\u6a5f\u60c5\u666f\uff0c\u5e6b\u52a9\u7528\u6236\u7406\u89e3\u53ef\u80fd\u7684\u7d50\u679c\u7bc4\u570d\u53ca\u5176\u6982\u7387\uff0c\u7279\u5225\u9069\u5408\u9700\u8981\u91cf\u5316\u98a8\u96aa\u6216\u4e0d\u78ba\u5b9a\u6027\u7684\u5834\u666f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"720\" style=\"aspect-ratio: 1280 \/ 720;\" width=\"1280\" autoplay loop muted 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class=\"wp-block-list\">\n<li>\u6bcf\u500b\u4efb\u52d9\u7684\u5b8c\u6210\u6642\u9593\u662f\u96a8\u6a5f\u7684\uff0c\u670d\u5f9e\u5747\u52fb\u5206\u5e03\u3002<\/li>\n\n\n\n<li>\u7e3d\u5b8c\u6210\u6642\u9593 = \u4efb\u52d9A\u6642\u9593 + \u4efb\u52d9B\u6642\u9593 + \u4efb\u52d9C\u6642\u9593\u3002<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u96a8\u6a5f\u62bd\u6a23<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5c0d\u6bcf\u500b\u4efb\u52d9\uff0c\u96a8\u6a5f\u751f\u6210\u4e00\u500b\u5b8c\u6210\u6642\u9593\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4efb\u52d9A\uff1a\u96a8\u6a5f\u6578\u5728[5, 7]\u4e4b\u9593\u3002<\/li>\n\n\n\n<li>\u4efb\u52d9B\uff1a\u96a8\u6a5f\u6578\u5728[3, 5]\u4e4b\u9593\u3002<\/li>\n\n\n\n<li>\u4efb\u52d9C\uff1a\u96a8\u6a5f\u6578\u5728[2, 4]\u4e4b\u9593\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6a21\u64ec\u8a66\u9a57<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u91cd\u890710,000\u6b21\uff0c\u6bcf\u6b21\u751f\u6210\u96a8\u6a5f\u7684\u4efb\u52d9\u6642\u9593\uff0c\u8a08\u7b97\u7e3d\u6642\u9593\u3002<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5206\u6790\u7d50\u679c<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6536\u96c6\u6240\u6709\u8a66\u9a57\u7684\u7e3d\u6642\u9593\uff0c\u8a08\u7b97\u983b\u7387\u5206\u5e03\u3002<\/li>\n\n\n\n<li>\u7528\u76f4\u65b9\u5716\u5c55\u793a\u7e3d\u6642\u9593\u7684\u6982\u7387\u5206\u5e03\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u6a21\u64ec\u7d50\u679c\u5c55\u793a<\/h4>\n\n\n\n<p>\u5047\u8a2d\u6211\u5011\u904b\u884c\u6a21\u64ec\uff0c\u5f97\u5230\u7e3d\u5b8c\u6210\u6642\u9593\u7684\u983b\u7387\u5206\u5e03\u3002\u4ee5\u4e0b\u662f\u4e00\u500b\u76f4\u65b9\u5716\uff0c\u986f\u793a\u7e3d\u5b8c\u6210\u6642\u9593\u7684\u5206\u5e03\uff08\u5047\u8a2d\u6578\u64da\u5df2\u6a21\u64ec\u751f\u6210\uff09\u3002<\/p>\n\n\n\n<div class=\"codecopy-container\">\n                <div class=\"codecopy-header\">\n                    \n                    <button class=\"codecopy-btn\" data-target=\"codecopy-69f8c25e2035e\" title=\"Copy code to clipboard\">\n                <svg width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n                    <path d=\"M16 1H4C2.9 1 2 1.9 2 3V17H4V3H16V1ZM19 5H8C6.9 5 6 5.9 6 7V21C6 22.1 6.9 23 8 23H19C20.1 23 21 22.1 21 21V7C21 5.9 20.1 5 19 5ZM19 21H8V7H19V21Z\" fill=\"currentColor\"\/>\n                <\/svg>\n                <span class=\"codecopy-text\">Copy<\/span>\n            <\/button>\n                <\/div>\n                <pre class=\"line-numbers\" id=\"codecopy-69f8c25e2035e\"><code class=\"language-text\">{\n  \"type\": \"histogram\",\n  \"data\": {\n    \"labels\": &#91;\"10\", \"10.5\", \"11\", \"11.5\", \"12\", \"12.5\", \"13\", \"13.5\", \"14\", \"14.5\", \"15\", \"15.5\", \"16\"],\n    \"datasets\": &#91;{\n      \"label\": \"\u7e3d\u5b8c\u6210\u6642\u9593\u983b\u7387\",\n      \"data\": &#91;50, 200, 600, 1200, 2000, 2500, 2200, 1500, 800, 400, 150, 50, 10],\n      \"backgroundColor\": \"rgba(54, 162, 235, 0.7)\",\n      \"borderColor\": \"rgba(54, 162, 235, 1)\",\n      \"borderWidth\": 1\n    }]\n  },\n  \"options\": {\n    \"scales\": {\n      \"x\": {\n        \"title\": {\n          \"display\": true,\n          \"text\": \"\u7e3d\u5b8c\u6210\u6642\u9593\uff08\u5929\uff09\"\n        }\n      },\n      \"y\": {\n        \"title\": {\n          \"display\": true,\n          \"text\": \"\u983b\u7387\"\n        }\n      }\n    },\n    \"plugins\": {\n      \"title\": {\n        \"display\": true,\n        \"text\": \"\u8499\u7279\u5361\u7f85\u6a21\u64ec\uff1a\u9805\u76ee\u5b8c\u6210\u6642\u9593\u5206\u5e03\"\n      }\n    }\n  }\n}<\/code><\/pre>\n            <\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u5716\u8868\u89e3\u91cb<\/h4>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-dominant-color=\"202f3a\" data-has-transparency=\"false\" style=\"--dominant-color: #202f3a;\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"581\" src=\"\/blog\/wp-content\/uploads\/2025\/07\/montecarlo1-1024x581.png\" alt=\"\" class=\"wp-image-5868 not-transparent\" srcset=\"https:\/\/infernews.com\/blog\/wp-content\/uploads\/2025\/07\/montecarlo1-1024x581.png 1024w, https:\/\/infernews.com\/blog\/wp-content\/uploads\/2025\/07\/montecarlo1-300x170.png 300w, https:\/\/infernews.com\/blog\/wp-content\/uploads\/2025\/07\/montecarlo1-768x436.png 768w, https:\/\/infernews.com\/blog\/wp-content\/uploads\/2025\/07\/montecarlo1-1536x871.png 1536w, https:\/\/infernews.com\/blog\/wp-content\/uploads\/2025\/07\/montecarlo1.png 1886w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>X\u8ef8<\/strong>\uff1a\u8868\u793a\u7e3d\u5b8c\u6210\u6642\u9593\uff08\u5929\uff09\uff0c\u7bc4\u570d\u5f9e10\u5929\u523016\u5929\uff08\u56e0\u70ba\u6700\u5c0f\u503c5+3+2=10\uff0c\u6700\u5927\u503c7+5+4=16\uff09\u3002<\/li>\n\n\n\n<li><strong>Y\u8ef8<\/strong>\uff1a\u8868\u793a\u8a72\u6642\u9593\u7bc4\u570d\u7684\u983b\u7387\uff08\u8a66\u9a57\u6b21\u6578\uff09\u3002<\/li>\n\n\n\n<li><strong>\u5206\u4f48\u5f62\u72c0<\/strong>\uff1a\u6a21\u64ec\u7d50\u679c\u986f\u793a\u7e3d\u5b8c\u6210\u6642\u9593\u5927\u591a\u96c6\u4e2d\u572812\u81f314\u5929\u4e4b\u9593\uff0c\u9019\u8868\u660e\u9805\u76ee\u5f88\u53ef\u80fd\u5728\u9019\u500b\u6642\u9593\u7bc4\u570d\u5167\u5b8c\u6210\u3002<\/li>\n\n\n\n<li><strong>\u6982\u7387\u5206\u6790<\/strong>\uff1a<\/li>\n\n\n\n<li>\u53ef\u4ee5\u5f9e\u5716\u8868\u63a8\u7b97\uff0c\u4f8b\u5982\uff0c90%\u7684\u8a66\u9a57\u7d50\u679c\u53ef\u80fd\u843d\u572811.5\u81f314.5\u5929\u4e4b\u9593\u3002<\/li>\n\n\n\n<li>\u5e73\u5747\u5b8c\u6210\u6642\u9593\u7d04\u70ba13\u5929\uff08\u53ef\u901a\u904e\u6a21\u64ec\u6578\u64da\u8a08\u7b97\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u6559\u5b78\u91cd\u9ede<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8f38\u5165\u4e0d\u78ba\u5b9a\u6027<\/strong>\uff1a\u6bcf\u500b\u4efb\u52d9\u7684\u6642\u9593\u4e0d\u662f\u56fa\u5b9a\u7684\uff0c\u800c\u662f\u96a8\u6a5f\u7684\uff0c\u6a21\u64ec\u771f\u5be6\u4e16\u754c\u7684\u4e0d\u78ba\u5b9a\u6027\u3002<\/li>\n\n\n\n<li><strong>\u5927\u91cf\u8a66\u9a57<\/strong>\uff1a10,000\u6b21\u8a66\u9a57\u78ba\u4fdd\u7d50\u679c\u7684\u7d71\u8a08\u53ef\u9760\u6027\u3002<\/li>\n\n\n\n<li><strong>\u8996\u89ba\u5316<\/strong>\uff1a\u76f4\u65b9\u5716\u6e05\u695a\u5c55\u793a\u7d50\u679c\u7684\u6982\u7387\u5206\u5e03\uff0c\u5e6b\u52a9\u6c7a\u7b56\u8005\u7406\u89e3\u98a8\u96aa\u548c\u53ef\u80fd\u6027\u3002<\/li>\n\n\n\n<li><strong>\u61c9\u7528\u5834\u666f<\/strong>\uff1a\u9019\u7a2e\u65b9\u6cd5\u53ef\u7528\u65bc\u9805\u76ee\u7ba1\u7406\u3001\u91d1\u878d\u98a8\u96aa\u5206\u6790\u3001\u5de5\u7a0b\u8a2d\u8a08\u7b49\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u5982\u4f55\u5be6\u73fe\u6a21\u64ec<\/h4>\n\n\n\n<p>\u4ee5\u4e0b\u662f\u4e00\u500b\u7c21\u55ae\u7684Python\u507d\u4ee3\u78bc\uff0c\u5c55\u793a\u5982\u4f55\u751f\u6210\u6a21\u64ec\u6578\u64da\uff08\u50c5\u4f9b\u53c3\u8003\uff0c\u7121\u9700\u57f7\u884c\uff09\uff1a<\/p>\n\n\n\n<div class=\"codecopy-container\">\n                <div class=\"codecopy-header\">\n                    \n                    <button class=\"codecopy-btn\" data-target=\"codecopy-69f8c25e203d5\" title=\"Copy code to clipboard\">\n                <svg width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n                    <path d=\"M16 1H4C2.9 1 2 1.9 2 3V17H4V3H16V1ZM19 5H8C6.9 5 6 5.9 6 7V21C6 22.1 6.9 23 8 23H19C20.1 23 21 22.1 21 21V7C21 5.9 20.1 5 19 5ZM19 21H8V7H19V21Z\" fill=\"currentColor\"\/>\n                <\/svg>\n                <span class=\"codecopy-text\">Copy<\/span>\n            <\/button>\n                <\/div>\n                <pre class=\"line-numbers\" id=\"codecopy-69f8c25e203d5\"><code class=\"language-text\">import numpy as np\nimport matplotlib.pyplot as plt\n\n# \u8a2d\u7f6e\u8a66\u9a57\u6b21\u6578\nn_trials = 10000\n# \u96a8\u6a5f\u62bd\u6a23\u4efb\u52d9\u6642\u9593\ntask_a = np.random.uniform(5, 7, n_trials)\ntask_b = np.random.uniform(3, 5, n_trials)\ntask_c = np.random.uniform(2, 4, n_trials)\n# \u8a08\u7b97\u7e3d\u6642\u9593\ntotal_time = task_a + task_b + task_c\n# \u7e6a\u88fd\u76f4\u65b9\u5716\nplt.hist(total_time, bins=30, density=True)\nplt.xlabel('\u7e3d\u5b8c\u6210\u6642\u9593\uff08\u5929\uff09')\nplt.ylabel('\u983b\u7387')\nplt.title('\u8499\u7279\u5361\u7f85\u6a21\u64ec\uff1a\u9805\u76ee\u5b8c\u6210\u6642\u9593\u5206\u5e03')\nplt.show()<\/code><\/pre>\n            <\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u7e3d\u7d50<\/h4>\n\n\n\n<p>\u9019\u500b\u6559\u5b78\u5c55\u793a\u4e86\u8499\u7279\u5361\u7f85\u6a21\u64ec\u7684\u57fa\u672c\u6d41\u7a0b\uff1a\u5b9a\u7fa9\u554f\u984c\u3001\u96a8\u6a5f\u62bd\u6a23\u3001\u591a\u6b21\u8a66\u9a57\u3001\u5206\u6790\u7d50\u679c\uff0c\u4e26\u901a\u904e\u76f4\u65b9\u5716\u8996\u89ba\u5316\u7d50\u679c\u3002\u9019\u7a2e\u65b9\u6cd5\u80fd\u6709\u6548\u8655\u7406\u4e0d\u78ba\u5b9a\u6027\uff0c\u5e6b\u52a9\u6c7a\u7b56\u8005\u66f4\u597d\u5730\u7406\u89e3\u98a8\u96aa\u548c\u53ef\u80fd\u6027\u3002<\/p>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"The most important skill in statistics | Monte Carlo Simulation\" style=\"width:853px;max-width:100%;margin:5px auto;\"><div class=\"lyMe\" id=\"WYL_r7cn3WS5x9c\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\"><div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2Fr7cn3WS5x9c%2Fhqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/r7cn3WS5x9c\" \/><meta itemprop=\"duration\" content=\"PT13M35S\" \/><meta itemprop=\"uploadDate\" content=\"2024-01-31T18:00:35Z\" \/><\/div><div id=\"lyte_r7cn3WS5x9c\" data-src=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2Fr7cn3WS5x9c%2Fhqdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">The most important skill in statistics | Monte Carlo Simulation<\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/r7cn3WS5x9c\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/infernews.com\/blog\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2Fr7cn3WS5x9c%2F0.jpg\" alt=\"The most important skill in statistics | Monte Carlo Simulation\" width=\"853\" height=\"460\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Simulation studies are a cornerstone of statistical research and a useful tool for learning statistics. \ud83d\udd17 LINKS MENTIONED: OTHER CHANNEL LINKS \ud83d\uddde\ufe0f Substack: https:\/\/verynormal.substack.com \ud83c\udfea My digital products: https:\/\/very-normal.sellfy.store \u2615 Buy me a Ko-fi: https:\/\/ko-fi.com\/verynormal\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:853px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>","protected":false},"excerpt":{"rendered":"<p>\u8499\u7279\u5361\u7f85\u6a21\u64ec\uff08Monte Carlo 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