设X1~N(1,2),X2~N(0,3),X3~N(2,1),X1,X2,X3相互独立,则P{0
问题描述:
设X1~N(1,2),X2~N(0,3),X3~N(2,1),X1,X2,X3相互独立,则P{0
答
设随机变量X=2X1+3X2-X3μ=EX=2E(X1)+3E(X2)-E(X3)=2×1+3×0-2=0σ²=4D(X1)+9D(X2)+D(X3)=4×2+9×3+1=36n(0,36)P﹛0<2X1+3X2-X3<6﹜=Φ﹛(6-0)/6﹜-Φ﹛(0﹣0)/6﹜=Φ(1﹚-Φ(0)查表可得P=0.3413...