{"action":"opened","issue":{"url":"https://api.github.com/repos/jiweiyuan/-/issues/1","repository_url":"https://api.github.com/repos/jiweiyuan/-","labels_url":"https://api.github.com/repos/jiweiyuan/-/issues/1/labels{/name}","comments_url":"https://api.github.com/repos/jiweiyuan/-/issues/1/comments","events_url":"https://api.github.com/repos/jiweiyuan/-/issues/1/events","html_url":"https://github.com/jiweiyuan/-/issues/1","id":357897765,"node_id":"MDU6SXNzdWUzNTc4OTc3NjU=","number":1,"title":"概率论与数理统计","user":{"login":"jiweiyuan","id":23147684,"node_id":"MDQ6VXNlcjIzMTQ3Njg0","avatar_url":"https://avatars2.githubusercontent.com/u/23147684?v=4","gravatar_id":"","url":"https://api.github.com/users/jiweiyuan","html_url":"https://github.com/jiweiyuan","followers_url":"https://api.github.com/users/jiweiyuan/followers","following_url":"https://api.github.com/users/jiweiyuan/following{/other_user}","gists_url":"https://api.github.com/users/jiweiyuan/gists{/gist_id}","starred_url":"https://api.github.com/users/jiweiyuan/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jiweiyuan/subscriptions","organizations_url":"https://api.github.com/users/jiweiyuan/orgs","repos_url":"https://api.github.com/users/jiweiyuan/repos","events_url":"https://api.github.com/users/jiweiyuan/events{/privacy}","received_events_url":"https://api.github.com/users/jiweiyuan/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":0,"created_at":"2018-09-07T02:37:36Z","updated_at":"2018-09-07T02:37:36Z","closed_at":null,"author_association":"OWNER","body":"#概率论和数理统计\r\n##随机变量\r\n###一维随机变量\r\n####一维离散型随机变量\r\n#####二项分布\r\n\r\n#####泊松分布$X\\sim(\\lambda)$\r\n泊松分布\r\n$$P(X=i)=e^{-\\lambda}\\lambda^i/i!$$\r\nX表示在一定的时间或者空间内出现的事件的个数这种场合\r\n$$\\begin{aligned}\r\nE(X)&=\\sum_{i=0}^{\\infty} i·e^{-\\lambda}\\lambda^i/i!\\\\\r\n&={\\lambda}e^{-\\lambda}\\sum_{i=1}^{\\infty}{{\\lambda^{i-1}}\\over{(i-1)!}}\\\\\r\n&={\\lambda}e^{-\\lambda}\\sum_{i=0}^{\\infty}{{\\lambda^i}\\over{i!}}\\\\\r\n&={\\lambda}e^{-\\lambda}e^{\\lambda}\\\\\r\n&=\\lambda\r\n\\end{aligned}\r\n$$\r\n$X\\sim P(\\lambda)$中$\\lambda$的意义指指定时间空间内事件发生的平均次数。\r\n\r\n####一维连续型随机变量\r\n##随机变量的数字特征\r\n###数学期望\r\n####数学期望的定义\r\n#####1、有限离散随机变量期望\r\n$$E(X)=a_1p_1+a_2p_2+···+a_mp_m$$\r\n#####2、无限离散随机变量期望\r\n若$\\sum_{i=1}^{\\infty}|a_i|p_i<\\infty$,则\r\n$$ E(X)=\\sum_{i=1}^{\\infty}a_ip_i$$\r\n#####3、连续随机变量期望\r\n若$\\int_{-\\infty}^{\\infty}|x|dx<\\infty$,则\r\n$$E(X)=\\int_{-\\infty}^{\\infty}xdx$$\r\n"}}
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