设随机变量X的概率密度函数为
f(x)=
{(3/2)x2，-1≤x≤1，
{0，其他
试求：(1)E(X)，D(X)；(2)P{|X-E(X)|＜2D(X)}.
(1)E(X)=∫1-1(3/2)x2dx=0， D(X)=E(X2)-E2(X)=∫1-1(3/2)x4dx=3/5 (2)P{|X-E(X)|}＜2D(X)}=P{|X|＜6/5}=∫6/5-(6/5)f(x)dx =∫1-1(3/2)x2dx=1
设随机变量X的概率密度函数为
f(x)=
{(3/2)x2，-1≤x≤1，
{0，其他
试求：(1)E(X)，D(X)；(2)P{|X-E(X)|＜2D(X)}.
(1)E(X)=∫1-1(3/2)x2dx=0， D(X)=E(X2)-E2(X)=∫1-1(3/2)x4dx=3/5 (2)P{|X-E(X)|}＜2D(X)}=P{|X|＜6/5}=∫6/5-(6/5)f(x)dx =∫1-1(3/2)x2dx=1
