Question

你好，高手，我这里有一个问答题不会， 设随机变量X的概率密度为f(x)={x/2,0<=X<=2; 0.其他

试求（1）E(X),D(X);
(2)D(2-3X)
(3)P{O<X<1}

Answer 1

(1)
①
EX=∫xf(x)dx
=∫x(x/2) dx
=(1/2)∫x²dx
= x³/6 |(从0到2)
= 4/3
②
EX²
=∫x²f(x)dx
= ∫x²(x/2)dx
= (1/2)∫x³dx
= x^4/8 |(从0到2)
=2
③
DX=EX²-(EX)² = 2 - (4/3)²= 2/9

(2)
E(2-3X)=2-3E(X)=-2;
D(2-3X)=9D(X)=2

(3)P{O<X<1}
=∫f(x)dx {由0积到1}
=∫(x/2)dx
=x²/4 |(0到1)
=1/4

Answer 2

2)D(2-3X)
(3)P{O<X<1}