D(X)=E(X)=10
由D(X)=E(X²)-[E(X)]²
得E(X²)=D(X)+[E(X)]²=10+10²=110
故P{X=E(X²)}=P{X=110}=(10^110)·e^(-110)/110!不好意思啊 題目錯了一個數(shù)據(jù)設(shè)隨機變量X~π(1）,則P{X=E(X^2)}=D(X)=E(X)=1由D(X)=E(X²)-[E(X)]²得E(X²)=D(X)+[E(X)]²=1+1²=2故P{X=E(X²)}=P{X=2}=(1^2)·e^(-1)/2!=1/(2e)