Question

对三架机床进行检验,各机床发上故障是相互独立的,且概率分别为P1,P2,P3,X为发生故障仪器的个数,则EX=

Answer 1

分析：

X为发生故障仪器的个数,X=0,1,2,3

P(X=0)=(1-P1)(1-P2)(1-P3)

P(X=1)=P1(1-P2)(1-P3)+(1-P1)P2(1-P3)+(1-P1)(1-P2)P3

P(X=2)=P1P2(1-P3)+(1-P1)P2P3+P1(1-P2)P3

P(X=3)=P1P2P3

则EX=0*P(X=0)+1*P(X=1)+2*P(X=2)+3*P(X=3)