Eξ,Dξ分别为随机变量ξ的数学期望与方差.由Dξ=E(ξ-Eξ)2=Eξ2-(Eξ)2≥0,知Eξ2≥(Eξ)2(*),当且仅当ξ可能取的值都相等时取等号.构造随机变量ξ的分布列,利用(*)式可以巧求一类题型的最小值.例1已知x,y,z∈R+,且2x+4y+7z=5,求2x+y4+7z的最小值.解构造ξ的分布列为 Eξ and Dξ are the mathematical expectation and variance of the random variable ξ, respectively, and Eξ2 ≥ (Eξ) 2 (*) is given by Dξ = E (ξ-Eξ) 2 = Eξ2- (Eξ) Equations may be taken equal when the equal sign. Constructing the distribution of random variable ξ, the use of (*) can be calculated by a type of minimum. Example 1 known x, y, z ∈ R +, and 2x + 4y + 7z = 5, find the minimum value of 2x + y4 + 7z. The distribution of solution structure ξ is listed as