泊松分布的数字特征EX=DX=λ而由方差D(X)=E(X²)-E(X)²,可得E(X²)=λ+λ²于是,E[(3X²+2X-1)]=E(3X²)+2E(X)-1=3(λ+λ²)+2λ-1=3λ²+5λ-1