随机变量的函数的数学期望

Mathematical Average Value of the Function of Random Variable

由“曲线分布密度”的公式φη(y) =∑kφξ(xk) |g′k(y) |和“曲面分布密度”的公式φζ(z) =∫czφ(g(y,z) ,y) |g′z(y,z) |dy,对有函数关系的随机变量η =f (ξ)及ζ =f (ξ,η)的数学期望公式 E(η) =∫φ(x) f (x) dx和 E(ζ) =∫∫f (x,y)φ(x,y) dxdy给出证明 。

The formula of mathematical average value of random variablehaving the traltionshop of function betweenη = f (ξ) andζ=f (ξ,η) ,E(η) =∫φ (x) f (x) dx and E(ζ) =∫∫f (x,y)φ(x,y) dxdy has been proved by the formulas of curcilinearand curved surface distribution density,i.e.φη(y) =∑ k φξ(xk) |g′k(y) |,φζ(z) =∫ czφ(g(y,z) ,y) |g′z(y,z) |dy. And several application of this formula has been provided in the paper.