Question

概率论,二维随机变量,均匀分布设二维随机变量（X,Y）在区域R:0≤x≤1,0≤y≤x上服从均匀分布,求：数学期望E（X

Answer 1

f(x,y) = A(x从0到1积分,这是外积分) {(y从0到x积分,这是内积分) dy} dx = 1

= A(x从0到1积分,这是外积分) xdx

= (A/2)(x^2)|代入x=1

= A/2

= 1 --> A=2.

即, f(x,y)=2, 0