设随机变量X~N(-1,3),U[2,4],E(4),X,Y,Z相互独立,求E(3X-2XY+YZ+Z-2),D(2X+3Y-2Z+3)
问题描述:
设随机变量X~N(-1,3),U[2,4],E(4),X,Y,Z相互独立,求E(3X-2XY+YZ+Z-2),D(2X+3Y-2Z+3)
答
EX = -1,DX = 3;EY = (2+4)/2 = 3,DY = (4-2)^2/12 = 1/3;EZ = 4^(-1) = 1/4,DZ = 4^(-2) = 1/16;E(3X-2XY+YZ+Z-2) = E(3X)-E(2XY)+E(YZ)+EZ-E(2) = 3EX-2EXEY+EYEZ+EZ-2 (X,Y,Z相互独立)= (代入可得结果)D(2X+3Y-2...