期望、方差、协方差、协方差矩阵 期望、方差、协方差和协方差矩阵

期望、方差、协方差和协方差矩阵

1.离散随机变量的X的数学期望:##

E ( X ) = k = 1 x k p k E ( X ) = k = 1 x k p k E ( X ) = k = 1 x k p k E(X)=∑∞k=1xkpkE(X)=∑k=1∞xkpk E(X) = \sum_{k=1}^{\infty}x_kp_k ρXY=0, 两个变量不相关
p6
p7



四、协方差矩阵

p8
推广到多维:
p9
对于连续的情况:
p0

例子:
可以参考下面的博客:
详解协方差与协方差矩阵:https://blog.csdn.net/ybdesire/article/details/6270328


参考: 概率论与数理统计 浙大

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	<div class="comment-list-box" style="max-height: none;"><ul class="comment-list"><li class="comment-line-box d-flex" data-commentid="9180922" data-replyname="weixin_42881002">        <a target="_blank" href="https://me.csdn.net/weixin_42881002"><img src="https://avatar.csdn.net/7/8/7/3_weixin_42881002.jpg" alt="weixin_42881002" class="avatar"></a>          <div class="right-box ">            <div class="info-box">              <a target="_blank" href="https://me.csdn.net/weixin_42881002"><span class="name ">weixin_42881002:</span></a>              <span class="comment">第二部分方差的计算实际常用公式有误。应该是DX=EX^2-(EX)^2</span><span class="date" title="2019-02-18 11:26:19">(1周前</span><span class="floor-num">#1楼)</span><span class="opt-box"><a class="btn btn-link-blue btn-read-reply" data-type="readreply">查看回复(1)</a><a class="btn btn-link-blue btn-report" data-type="report">举报</a><a class="btn btn-link-blue btn-reply" data-type="reply">回复</a></span></div>          </div>        </li><li class="replay-box"><ul class="comment-list"><li class="comment-line-box d-flex" data-commentid="9181128" data-replyname="qq_23869697">        <a target="_blank" href="https://me.csdn.net/qq_23869697"><img src="https://avatar.csdn.net/A/2/F/3_qq_23869697.jpg" alt="qq_23869697" class="avatar"></a>          <div class="right-box reply-box">            <div class="info-box">              <a target="_blank" href="https://me.csdn.net/qq_23869697"><span class="name mr-8">siucaan</span></a>回复  <span class="name">weixin_42881002:</span>              <span class="comment">你是对的,我修改了,谢谢。</span><span class="date" title="2019-02-18 12:02:30">(1周前</span>)<span class="opt-box"><a class="btn btn-link-blue btn-report" data-type="report">举报</a><a class="btn btn-link-blue btn-reply" data-type="reply">回复</a></span></div>          </div>        </li></ul></li></ul></div>
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					向量的<em>期望</em>值、均值向量和<em>协方差</em>矩阵				</h4>
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					<span class="date hover-show">04-12</span>
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						<span class="desc oneline">向量随机变量X的数学期望也是一个向量,其各分量是原X的各个分量的数学期望。如果f(x)是d维随机变量X的n维向量函数&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;...</span>
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