设随机变量X，Y相互独立，它们的概率密度分别为
fX(x)=
{2e2x,x﹥0,
0，x≤0，
fY(y)=
{4,0≤x≤1/4,
0，其他．
求D(X+Y)．
E(X+Y)=E(X)+E(Y)=∫+∞02xe-2xdx+∫1/404ydy=1/2+1/8=5/8 E[(X+Y)2]=E(X2)+E(Y2)+2E(X)•E(Y)=∫+∞02x2e-2xdx+∫1/404y2dy+2∫+∞02xe-2xdx•∫1/404ydy=1/2+1/48+2×1/2×1/8=31/48 ∴D(X+Y)=E(X+Y)2]-E2(X+Y)=31/48-25/64=49/192
