Question

连续型随机变量x的分布函数为F(x)＝{0,x≤0 Ax³,0＜x≤2 1,x＞2？

连续型随机变量x的分布函数为F(x)＝{0,x≤0 Ax³,0＜x≤2 1,x＞2
求:(1)常数A的值？
(2)p{0＜x＜1},p{1.5＜x≤3}？

Answer 1

1) ∫ [0,2] Ax³ = 1 ==> A = 1/4
2) ∫ [0,1] x³/4 dx = 1/16
3) ∫ [1.5,2] x³/4 dx = 1 - 1.5^3/16 = 101/128