设二维随机变量(X,Y)的概率分布为 若随机事件{X=0}与{X+Y=1}相互独立,则a= 设二维随机变量（X，Y） 的概率分布为 XY 0 1...
\u8bbe\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf(X,Y)\u7684\u6982\u7387\u5206\u5e03\u4e3a \u82e5\u968f\u673a\u4e8b\u4ef6{X=0}\u4e0e{X+Y=1}\u76f8\u4e92\u72ec\u7acb,\u5219a=_____,b=P(X=0)=1/2+b,P(X+Y=1)=a+b,P(X=0,X+Y=1)=b
\u2235{X=0}\u4e0e{X+Y=1}\u76f8\u4e92\u72ec\u7acb
\u2234P(X=0)\u00b7P(X+Y=1)=P(X=0,X+Y=1)
\u2234(1/2+b)(a+b)=b
\u53c8\u2235 1/2+1/4+a+b=1
\u6240\u4ee5\uff1aa=1/12 b=1/6
\u6269\u5c55\u8d44\u6599
\u4e00\u822c\uff0c\u8bbeE\u662f\u4e00\u4e2a\u968f\u673a\u8bd5\u9a8c\uff0c\u5b83\u7684\u6837\u672c\u7a7a\u95f4\u662fS={e}\uff0c\u8bbeX=X\uff08e\uff09\u548cY=Y(e)S\u662f\u5b9a\u4e49\u5728S\u4e0a\u7684\u968f\u673a\u53d8\u91cf\uff0c\u7531\u5b83\u4eec\u6784\u6210\u7684\u4e00\u4e2a\u5411\u91cf\uff08X\uff0cY\uff09\uff0c\u53eb\u505a\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf\u6216\u4e8c\u7ef4\u968f\u673a\u5411\u91cf\u3002
\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf( X,Y)\u7684\u6027\u8d28\u4e0d\u4ec5\u4e0eX \u3001Y \u6709\u5173,\u800c\u4e14\u8fd8\u4f9d\u8d56\u4e8e\u8fd9\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u7684\u76f8\u4e92\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u9010\u4e2a\u5730\u6765\u7814\u7a76X\u6216Y\u7684\u6027\u8d28\u662f\u4e0d\u591f\u7684\uff0c\u8fd8\u9700\u5c06\uff08X\uff0cY\uff09\u4f5c\u4e3a\u4e00\u4e2a\u6574\u4f53\u6765\u7814\u7a76\u3002
\u7531\u9898\u8bbe\u53ef\u77e5\uff1aa+b+0.4+0.1=1\uff0c\u2460\u2235\u4e8b\u4ef6{X=0}\u4e0e{X+Y=1}\u76f8\u4e92\u72ec\u7acb\uff0c\u2234P{X=0\uff0cX+Y=1}=P{X=0}P{X+Y=1}\uff0c\u5373\uff1aa=\uff080.4+a\uff09\u00d7\uff08a+b\uff09\uff0c\u2461\u7531\u2460\uff0c\u2461\u53ef\u89e3\u5f97\uff1aa=0.4 b=0.1\uff0c\u6545\u5e94\u9009\uff1aB\uff0e
简单计算一下即可，答案如图所示
a=0.4,b=0.1
事件独立有P{X=0,X+Y=1}=P{X=0,Y=1}=P{X=0}*P{X+Y=1}
得出a=(0.4+a)*(a+b)
同时有0.4+a+b+0.1=1
最后有a=0.4,b=0.1
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