速成 on 海上共明月

速成 on 海上共明月https://withlia.cn/tags/%E9%80%9F%E6%88%90/Recent content in 速成 on 海上共明月Hugo -- gohugo.iozh-cnWed, 08 Jul 2026 20:44:55 +0800概率论与数理统计https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/Wed, 08 Jul 2026 20:44:55 +0800https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/<img src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/0.png" alt="Featured image of post 概率论与数理统计" /><p>本笔记基于 <a class="link" href="https://space.bilibili.com/661141753" target="_blank" rel="noopener" >框框老师</a> 的《概率论与数理统计》4 小时速成课整理，每一节配一张手写笔记图，方便快速回顾。</p> <blockquote> <p>视频原址：<a class="link" href="https://www.bilibili.com/video/BV168411Z7pf/" target="_blank" rel="noopener" >https://www.bilibili.com/video/BV168411Z7pf/</a></p> </blockquote> <hr> <h2 id="第一章随机事件及其概率一">第一章：随机事件及其概率（一） </h2> <div class="video-wrapper"> <iframe src="https://player.bilibili.com/player.html?as_wide=1&high_quality=1&page=1&bvid=BV168411Z7pf" scrolling="no" frameborder="no" framespacing="0" allowfullscreen="true" > </iframe> </div> <p><img alt="第一章：随机事件及其概率（一）" class="gallery-image" data-flex-basis="167px" data-flex-grow="69" height="1600" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px" src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/1.jpg" srcset="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/1_hu_61f8f8fde706183.jpg 800w, https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/1.jpg 1116w" width="1116"></p> <h2 id="第一章随机事件及其概率二">第一章：随机事件及其概率（二） </h2> <div class="video-wrapper"> <iframe src="https://player.bilibili.com/player.html?as_wide=1&high_quality=1&page=2&bvid=BV168411Z7pf" scrolling="no" frameborder="no" framespacing="0" allowfullscreen="true" > </iframe> </div> <p><img alt="第一章：随机事件及其概率（二）" class="gallery-image" data-flex-basis="168px" data-flex-grow="70" height="1600" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px" src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/2.jpg" srcset="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/2_hu_b64bbe416138221a.jpg 800w, https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/2.jpg 1122w" width="1122"></p> <h2 id="第二章一维随机变量及其分布一">第二章：一维随机变量及其分布（一） </h2> <div class="video-wrapper"> <iframe src="https://player.bilibili.com/player.html?as_wide=1&high_quality=1&page=4&bvid=BV168411Z7pf" scrolling="no" frameborder="no" framespacing="0" allowfullscreen="true" > </iframe> </div> <p><img alt="第二章：一维随机变量及其分布（一）" class="gallery-image" data-flex-basis="178px" data-flex-grow="74" height="1600" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px" src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/3.jpg" srcset="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/3_hu_80c398415dece576.jpg 800w, https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/3.jpg 1190w" width="1190"></p> <h2 id="第二章一维随机变量及其分布二">第二章：一维随机变量及其分布（二） </h2> <div class="video-wrapper"> <iframe src="https://player.bilibili.com/player.html?as_wide=1&high_quality=1&page=5&bvid=BV168411Z7pf" scrolling="no" frameborder="no" framespacing="0" allowfullscreen="true" > </iframe> </div> <p><img alt="第二章：一维随机变量及其分布（二）" class="gallery-image" data-flex-basis="175px" data-flex-grow="73" height="1600" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px" src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/4.jpg" srcset="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/4_hu_515e48644a739479.jpg 800w, https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/4.jpg 1172w" width="1172"></p> <h2 id="第三章二维随机变量及其分布">第三章：二维随机变量及其分布 </h2> <div class="video-wrapper"> <iframe src="https://player.bilibili.com/player.html?as_wide=1&high_quality=1&page=6&bvid=BV168411Z7pf" scrolling="no" frameborder="no" framespacing="0" allowfullscreen="true" > </iframe> </div> <p><img alt="第三章：二维随机变量及其分布" class="gallery-image" data-flex-basis="188px" data-flex-grow="78" height="1600" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px" src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/5.jpg" srcset="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/5_hu_a0434c0d080e4c3d.jpg 800w, https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/5.jpg 1254w" width="1254"></p> <h2 id="第四章随机变量的数字特征">第四章：随机变量的数字特征 </h2> <div class="video-wrapper"> <iframe src="https://player.bilibili.com/player.html?as_wide=1&high_quality=1&page=7&bvid=BV168411Z7pf" scrolling="no" frameborder="no" framespacing="0" allowfullscreen="true" > </iframe> </div> <p><img alt="第四章：随机变量的数字特征" class="gallery-image" data-flex-basis="175px" data-flex-grow="73" height="1600" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px" src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/6.jpg" srcset="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/6_hu_cd16d9356783d3fb.jpg 800w, https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/6.jpg 1172w" width="1172"></p> <h2 id="第五六章中心极限定理与数理统计基本概念">第五、六章：中心极限定理与数理统计基本概念 </h2> <div class="video-wrapper"> <iframe src="https://player.bilibili.com/player.html?as_wide=1&high_quality=1&page=8&bvid=BV168411Z7pf" scrolling="no" frameborder="no" framespacing="0" allowfullscreen="true" > </iframe> </div> <p><img alt="第五、六章：中心极限定理与数理统计基本概念" class="gallery-image" data-flex-basis="179px" data-flex-grow="74" height="1600" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px" src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/7.jpg" srcset="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/7_hu_1faaebf786650d5a.jpg 800w, https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/7.jpg 1196w" width="1196"></p> <h2 id="第七章参数估计">第七章：参数估计 </h2> <div class="video-wrapper"> <iframe src="https://player.bilibili.com/player.html?as_wide=1&high_quality=1&page=9&bvid=BV168411Z7pf" scrolling="no" frameborder="no" framespacing="0" allowfullscreen="true" > </iframe> </div> <p><img alt="第七章：参数估计" class="gallery-image" data-flex-basis="175px" data-flex-grow="73" height="1600" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px" src="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/8.jpg" srcset="https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/8_hu_525f195b32b22e3e.jpg 800w, https://withlia.cn/p/%E6%A6%82%E7%8E%87%E8%AE%BA%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/8.jpg 1170w" width="1170"></p>