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)}．
(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
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)}．
(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
