1.设x和y的相关系数为:Cxy
Cxy = E[(x-Ex)(y-Ey)] / (sigmx*sigmy)
= E[(x-Ex)(0.8x+0.7-0.8Ex-0.7)] / [sigmx*0.8*sigmx]
= E[0.8(x-Ex)(x-Ex)] / (0.8*sigm^2x)
= 0.8sigm^2x / (0.8*sigm^2x)
= 1
2.设X与Y相互独立且都服从标准正态分布,则 P(min(X,Y)>=0)=0.25 这个是怎么算出来的?
由于X与Y相互独立且都服从标准正态分布,它们联合概率密度函数为:
f(x,y) = 1/(2π) exp[-(x^2+y^2)/2]
那么
P(x,y>=0)=1/√(2π) ∫(0→∞)exp(-x^2/2)dx (1√(2π))∫(0→∞)exp(-y^2/2)dy
= 0.5×0.5 = 0.25