设随机变量X的概率密度函数为f(x)={3/2x2,-1≤x≤1,0，其他．试求：(1)E(X)，D(X)；(2)P{∣X-E(

设随机变量X的概率密度函数为
f(x)=
{3/2x²,-1≤x≤1,
0，其他．
试求：(1)E(X)，D(X)；(2)P{∣X-E(X)∣﹤2D(X)}．
【正确答案】：(1)E(X)=∫¹_-1(3/2)x³dx=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