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).
【正确答案】:(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
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(
- 2024-11-07 16:24:22
- 概率论与数理统计(工)(13174)
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