设随机变量x服从以1为参数的指数分布，记y=2x，求EY DY
\u6307\u6570\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b \u5df2\u77e5X\u670d\u4ece\u53c2\u6570\u4e3a1\u7684\u6307\u6570\u5206\u5e03 Y=X+e^(-2X) \u6c42EY\u4e0eDY \u6c42\u5927\u795e\u4eec\u5e2e\u5e2e\u5fd9\u554a\u63d0\u793a\uff1aEY=E(X+e^(-2X))=EX+E(e^-2X)
\u524d\u9762\u7684EX=1\uff0c\u540e\u9762\u7684\u5f0f\u5b50\u6839\u636e\u671f\u671b\u7684\u5b9a\u4e49\u5f0f\u3002\u6c42\u51fa
\u4e0d\u7406\u89e3\uff0c\u53ef\u4ee5\u7ee7\u7eed\u63d0\u95ee
X+Y=8 ==> Y=8-X,
X~B(10,0.6),
EX=0*C0.6^0*0.4^10+1*C0.6^1*0.4^9+2*C0.6^2*0.4^8+...
+10*C0.6^10*0.4^0=10*0.6=6,
EX^2=EX(X-1)+EX=10(10-1)0.6^2+6=32.4+6=38.4,
DX=EX^2-(EX)^2=38.4-36=10*0.6*0.4=2.4,
EY=E(8-X)=8-EX=8-6=2,
EY^2=E(8-X)^2=E(8^2-16X+X^2)=E64-16EX+EX^2=64-16*6+38.4=6.4,
DY= EY^2-(EY)^2=6.4-4=2.4
\u6216 DY=D(8-X)=D[8+(-X)]=D8+D(-X)=0+[(-1)^2]DX=DX=2.4
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