两个相互独立随机变量X,Y，X服从B(2,p),Y服从exp(λ),Z=X+Y,求Z的概率密度函数。
\u8bbe\u968f\u673a\u53d8\u91cfx\u670d\u4ece(-2,2)\u4e0a\u7684\u5747\u5300\u5206\u5e03\uff0c\u5219\u968f\u673a\u53d8\u91cfY=X^2\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e3aFy(y)=P{Y\u2264y}=P{X^2\u2264y}
\u5f53y<0\u65f6\uff0cFy\uff08y\uff09=0
\u5f530\u2264y\uff1c4\u65f6
Fy(y)=P{Y\u2264y}=P{X^2\u2264y}=P{\u221ay\u2264x\u2264\u221ay}=Fx(\u221ay)-Fx(-\u221ay)
\u5f53y\u22654\u65f6\uff0cFy(y)=1
\u6240\u4ee5\u5bf9Fy(y)\u6c42\u5bfc
fy(y)=[fx(\u221ay)+fx(-\u221ay)](1/(2\u221ay))=1/2*1/(2\u221ay)=1/(4\u221ay) 0\u2264y\uff1c4
fy(y)=0 \u5176\u4ed6
1.\u5148\u63d0\u9192\u4e00\u4e0b\uff0c\u9898\u76ee\u6982\u7387\u5bc6\u5ea6\u51fd\u6570f\uff08x\uff09\u5c11\u6253\u4e86\u4e00\u4e2a\u53d8\u91cf\uff0c\u5e94\u8be5\u662ff\uff08x\uff0cy\uff09
2.\u6bd4\u8f83\u4e8c\u7ef4\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u516c\u5f0f\u53ef\u4ee5\u53d1\u73b0\uff0cr=0\uff0c\u03bc1=\u03bc2=0\uff0c\u03c31=\u03c32=10\u3002
\u6240\u4ee5x\uff0cy\u670d\u4ece\u4e8c\u7ef4\u6b63\u6001\u5206\u5e03N\uff080,0,100,100,0\uff09
3.\u9898\u76ee\u4e2da\u662f\u53ef\u4ee5\u901a\u8fc7f\uff08x\uff0cy\uff09\u4e8c\u91cd\u79ef\u5206\u7b49\u4e8e=1\u6c42\u51fa\u6765\u7684\uff0c\u4e0d\u8fc7\u6b64\u9898\u4e0d\u9700\u8981\u505a\u8fd9\u4e2a\u4e8b\u60c5
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