Question

123456对应A1A2A3A4A5,够成一行排列,X是满足Ai=i（i＝12345）个数,求X期望

Answer 1

P(X=5)=1/5!=1/120

P(X=4)=0

P(X=3)=C(5,3)/5!=10/120

P(X=2)=C(5,2)*2/5!=20/120

P(X=1)=C(5,1)*3*3/5!=45/120

P(X=0)=1-1/120-10/120-20/120-45/120=44/120

E(X)=5*1/120+3*10/120+2*20/120+1*44/120=119/120