Question

一件机器由三大件构成在设备运转过程中各部件需要调整的概率为0.1 0.2和0.3假设各部件的状

Answer 1

设A,B,C是三个需要调整的部件,调整概率分别为0.1,0.2,0.3

计算概率：

X=0,概率：(1-0.1)*(1-0.2)*(1-0.3)=0.5040

X=1,概率：0.1*(1-0.2)*(1-0.3)+0.2*(1-0.1)*(1-0.3)+0.3*(1-0.1)*(1-0.2)=0.1327

X=2,概率：0.1*0.2*(1-0.3)+0.1*0.3*(1-0.2)+0.2*0.3*(1-0.1)=0.0980

X=3,概率：0.1*0.2*0.3=0.006

E(X)=1*0.1327+2*0.0980+3*0.006=0.612

E(X^2)=!^2*0.1327+2^2*0.0980+3^2*0.006=0.398

D(X)=E(X^2)-(E(X))^2=0.398-0.612^2=0.0235