Question

关于概率论问题一台设备由三大部件构成 在设备运转中各部件需要调整的概率相应为0.1,0.2,0.3 假设各部件的状态相互

Answer 1

部件数为X,X=0,1,2,3

X=0时,P(X)=0.9*0.8*0.7=0.504

X=1时,P(X)=0.1*0.8*0.7+0.9*0.2*0.7+0.9*0.8*0.3=0.398

X=2时,P(X)=0.1*0.2*0.7+0.1*0.8*0.3+0.9*0.2*0.3=0.092

X=3时,P(X)=0.1*0.2*0.3=0.006,

E(X)=0*0.504+1*0.398+2*0.092+3*0.006=0.6

D(X)=(0-0.6)^2*0.504+(1-0.6)^2*0.398+(2-0.6)^2*0.092+(3-0.6)^2*0.006

=0.46