设随机变量X~B(n,0.2),且D(0.5X-1)=0.32,则n等于多少

\u8bbe\u968f\u673a\u53d8\u91cfX~N\uff082\uff0c4\uff09\uff0c\u5219D\uff080.5X\uff09

\u968f\u673a\u53d8\u91cfX~N\uff082\uff0c4\uff09\uff0c\u6240\u4ee5D\uff08X)=4,D(0.5X)=0.5*0.5D(X)=0.25D(X)=1

\u4f60\u597d\uff1a
\u89e3\uff1a
\u7531\u9898\u610f\u5f97
u=3\uff0c\u03c3=1
\u90a3\u4e48
P\uff08-1\uff1cx\uff1c1\uff09
=fai\uff081-3\uff09/1-fai\uff08-1-3\uff09/1
=fai\uff08-2)-fai\uff08-4\uff09
\u518d\u6839\u636e\u67e5\u8868\uff0c\u5c31\u53ef\u4ee5\u5f97\u5230
P\u7684\u503c\u4e86

由已知，DX=n*0.2*0.8=0.16n,而D(0.5X-1)=0.5^2DX=0.25DX=0.25*0.16n=0.32,即可求n

璁鹃殢鏈哄彉閲廥~B(n,0.2),涓擠(0.5X-1)=0.32,鍒檔绛変簬澶氬皯
绛旓細鐢卞凡鐭ワ紝DX=n*0.2*0.8=0.16n,鑰孌(0.5X-1)=0.5^2DX=0.25DX=0.25*0.16n=0.32,鍗冲彲姹俷

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