Question

一个概率论与数理统计的题目,设随机变量X的概率密度为f(x)＝c*x^2 x大于等于-2,小于等于20 其他 试求：(1

Answer 1

1.对f(x)在[2,-2]积分,得原函数F(x)=1/3*c*x^3（2,-2）=1,

推出c=3/16

2.E(x)=对xf(x)在[-2,2]积分,解得E(x)=0,

E(x^2)=对x^2f(x)在[-2,2]积分,解得E（x^2）=3/5,

所以,D(x)=E(x^2)-E^2(x)=3/5

3.P{|X-E(X)|