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Original file line number Diff line number Diff line change
Expand Up @@ -406,7 +406,7 @@
"**伯努利模型的极大似然估计:** \n",
"定义$P(Y=1)$概率为$p$,可得似然函数为:$$L(p)=f_D(y_1,y_2,\\cdots,y_n|\\theta)=\\binom{n}{k}p^k(1-p)^{(n-k)}$$方程两边同时对$p$求导,则:$$\\begin{aligned}\n",
"0 & = \\binom{n}{k}[kp^{k-1}(1-p)^{(n-k)}-(n-k)p^k(1-p)^{(n-k-1)}]\\\\\n",
"& = \\binom{n}{k}[p^{(k-1)}(1-p)^{(n-k-1)}(m-kp)]\n",
"& = \\binom{n}{k}[p^{(k-1)}(1-p)^{(n-k-1)}(k-np)]\n",
"\\end{aligned}$$可解出$p$的值为$p=0,p=1,p=k/n$,显然$\\displaystyle P(Y=1)=p=\\frac{k}{n}$ \n",
"\n",
"**伯努利模型的贝叶斯估计:** \n",
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