设随机变量X的概率密度为
f(x)=
{2e-2x,x﹥0,
0,x≤0.
(1)求E(X)，D(X)；
(2)令y=[X-E(X)]/√D(X)，求Y的概率密度fY(y)．
(1)E(X)=∫+∞02xe-2xdx=1/2， E(X2)=∫+∞02x2e-2xdx=1/2 ∴D(X)=E(X2)-E2(X)=1/2-1/4 =1/4 (2)Y[X-E(X)]/√D(X)=(X-1/2)/1/2=2X-1 由y=2X-1得x=(1+y)/2，x＇=1/2 ∴fY(y)= {2e-(1+y)•(1/2) (1+y)/2﹥0 0 (1+y)/2≤ = {e-(1+y) y﹥-1 0 y≤-1
