[課業]機率作業
第三題我放棄(掩面)
以下答案僅供參考，錯了不負責
中文題:
(1)
即 1 - P(三個都不通電) = 1 - 0.4*0.2*0.1 = 0.992 //請拿小算盤驗證一下
(2)
0.6*0.2*0.1 + 0.4*0.8*0.1 + 0.4*0.2*0.9 = 0.116
EX4.
A random number is select from(0,π/2)
what is the probability that is sine is greater than its cosine?
-> 我這題沒想出數學上的証明 只想到說畫個sin和cos的圖...答案很明顯(?)
EX5.
Let x be a random variable.
Assume that the distribution function
F(x) = 0, if x<1
F(x) = (x^2-1)/8 , if 1≦x<3
F(x) = 1, if x≧3
1. Find and graph the density df(x)/dx = f(x) //即PDF的圖
2. Find x such that probability
-> 這題要倒過來做 先求出第二小題才能畫第一小題的圖
因為 PDF = CDF的微分
所以 f(x) = 0 , if x<1
f(x) = x/4 , if 1≦x<3 //我微分不行Orz 這邊可以的話驗算看看Q_Q
f(x) = 0 , if x≧3
所以 ╱
↑ ╱ 圖大概長這樣 注意一下相對應的值
│ ╱
1/4│ ╱
│
│───────→
1 3
EX2:
A bag initially contains three black balls and two white balls
1. Alternatively, if the ball drawn from the bag is white
then it's put back in the bag , other wise it's left out
Draw a trellis diagram that illustrates
the outcome space of this experiment
2. Find the probability of the sequence wwww and bbww for the experiment
given in (ii) .
Note that white and black are the balls drawn out first in
the sequence wwww and bbww respectively
ANS 1.
我覺得可能是我沒看懂題目(?) 我畫不出所有的樣本 因為白球會丟回去...
大致上是這樣:
www........bbb
www.......bwbb ....... 很多 = =">
www.......bwwb
ANS 2.
(a)wwww: 2/5 * 2/5 * 2/5 * 2/5 = 16/625
(b)bbww: 3/5 * 2/4 * 2/3 * 2/3 = 2/15
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※ 編輯: gingkoginkgo 來自: 203.68.15.28 (05/14 01:58)
※ 編輯: gingkoginkgo 來自: 203.68.15.28 (05/14 01:58)
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05/14 02:42, , 1F
05/14 02:42, 1F
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