二维随机变量XY的联合密度函数为F(x,y)=Ke^-(2x+y) X>0,y>0 O,求系数K

题目

二维随机变量XY的联合密度函数为F(x,y)=Ke^-(2x+y) X>0,y>0 O,求系数K

答案

x(0,正无穷)y(0,正无穷)F(x,y) = x(0,正无穷)(-Ke^(-2x+y)(y=+无穷)+Ke^(-2x+y)(y=0))
=x(0,正无穷)(0+ke^-2x)
=-K/2e^-2x(x=+无穷) + k/2*e^-2x(x=0)
=k/2 = 1
K=2