以X表示一周5天内机器发生故障的天数,则X-B(5,0.2),于是X有概率分布P(X=k)=C0.2k0.85-k,k=0,1,2,3,4,5. 以Y表示一周内所获利润,则 Y=g(X)= Y的概率分布为: P(Y=10)=P(X=0)=0.85=0.328 P(Y=5)=P(X=1)=C0.2·0.84=0.410 P(Y=0)=P(X=2)=C·0.22·0.83=0.205 P(Y=-2)=P(X≥3)=1-P(X=0)-P(X=1)-P(X=2)=0.057 故一周内的期望利润为: EY=10×0.328+5×0.410+0×0.205-2×0.057=5.216(万元) |