有一公司平均每20天接到6筆訂單,假設接單的間隔天數為指數分配,試問
1.3天內接到下一筆訂單的機率為何
2.至少需要5天才能接到下一筆的訂單的機率為何
數學機率問題如題目
2008-04-20 7:37 pm
回答 (2)
2008-04-24 4:16 am
✔ 最佳答案
λ= 6/20 =0.3 (平均每天所接到的訂單)f(x)=0.3e-0.3x ,x >0
(1) P(x<=3)=
∫<下限=0,上限=3> (0.3e-0.3x) dx = (-e-0.3x｜<下限=0上限=3>)
=1-e-0.9 =0.5934
(2)
P(X>=5)=∫<下限=5,上限=∞> (0.3e-0.3x) dx
=[-e-0.3x <下限=5, 上限=∞>]= (-e-∞)-(-e-1.5)=0+ e-1.5=0.2231
2008-04-20 10:09 pm
平均每20天接到6筆訂單
E[X] = 20/6 = 1/k , k = 3/10 = 0.3
1. F(x) = S_[0,x] ke^-kx dx 原本指數累積分布函數的樣子
F(3) = P(X=<3)
= S_[0,3] (0.3)e^-(0.3)x dx
= 1- 1/e^0.9
2. 1 - F(5) = P(X>=5)
= S_[5,oo] (0.3)e^-(0.3)x dx
= 1/e^1.5
E[X] = 20/6 = 1/k , k = 3/10 = 0.3
1. F(x) = S_[0,x] ke^-kx dx 原本指數累積分布函數的樣子
F(3) = P(X=<3)
= S_[0,3] (0.3)e^-(0.3)x dx
= 1- 1/e^0.9
2. 1 - F(5) = P(X>=5)
= S_[5,oo] (0.3)e^-(0.3)x dx
= 1/e^1.5
收錄日期: 2021-04-30 11:39:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080420000015KK03841