簡單2條PROB題...緊急

👨🏻‍🏫 學術台數學

[匿名]

2015-04-29 4:57 am

Please list the step,thanks
http://postimg.org/image/gxzpfircp/

更新1:

第一題... suppose a bin contains n>=2 balls, one red and n-1 black. you and i takes turn to draw a ball randomly from bin WITH REPLACEMENT.whoever draw the red ball first win.Do i have an advantage over you???? if o,how much advantage do i have?i.e.P(first player wins)=?

更新2:

可以的話第二題可以列step嗎???太difficult,想不到~~~thanks

更新3:

https://hk.knowledge.yahoo.com/question/question?qid=7015042800012

更新4:

https://hk.knowledge.yahoo.com/question/question?qid=7015042800008

更新5:

https://hk.knowledge.yahoo.com/question/question?qid=7015042800006

更新6:

https://hk.knowledge.yahoo.com/question/question?qid=7015042700112

更新7:

https://hk.knowledge.yahoo.com/question/question?qid=7015042700113

更新8:

yup~~~

更新9:

sor仲有依幾題想check答案,時間較短(因為仲有幾日就考啦) https://hk.knowledge.yahoo.com/question/question?qid=7015050300054 https://hk.knowledge.yahoo.com/question/question?qid=7015050300053 https://hk.knowledge.yahoo.com/question/question?qid=7015050300052 幫幫手,thanks

更新10:

當然可以吧,無利益涉及~其實分享都唔係犯法lol 所以都唔使擔心有人會知... 不過等我考完試先send

更新11:

找到最後幾條題目: https://hk.knowledge.yahoo.com/question/question?qid=7015050300065&mode=w&from=question&recommend=0&.crumb=rDpKhkKp4wR THANKS~

回答 (2)

知足常樂

2015-05-04 2:12 am

✔ 最佳答案

第一題唔知你問乜~

第二題要 convolution, 唔 straightforward, 但你可以先考慮 n = 2, 3, 4 的情況。

2015-05-03 05:58:31 補充：
是否 HKUST 的題？？？

2015-05-03 16:07:22 補充：
明白明白～～～～～～～～

2015-05-03 17:06:24 補充：
哈～　我竟然估中左係 HKUST 的題～
呢ｄ題目出得幾好，我幾鍾意～

你呢條第二題實在太難了～
大家都答不到你～

2015-05-03 17:12:38 補充：
PS：
其實為何你要匿名發問？
都無人知道你是誰～
不必浪費匿名的點數嘛～

你是很有責任感的同學，帖子都沒有放棄，而且跟進得很快～

不知道是否方便分享更多的 past paper 給我參考？
分享完畢後可以刪掉，沒有人會知～
Thanks~

2015-05-03 17:19:03 補充：
謝謝你！！

╭∧---∧╮
│ .✪‿✪ │
╰/) ⋈ (\\╯

2015-05-03 18:12:53 補充：
Please read:

http://postimg.org/image/insksad2j/

Information about Irwin-Hall distribution:

http://www.math.uah.edu/stat/special/IrwinHall.html

http://global.oup.com/us/companion.websites/9780195089653/pdf/SolutionsManual.pdf

http://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution

Irwin-Hall distribution
Probability density function
圖片參考：https://s.yimg.com/lo/api/res/1.2/iTaG41dBde.wxzXUdn69bw--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://upload.wikimedia.org/wikipedia/en/thumb/2/23/Irwin-hall-pdf.svg/276px-Irwin-hall-pdf.svg.png

Cumulative distribution function
圖片參考：https://s.yimg.com/lo/api/res/1.2/AGx.eIIX9qiIa2BHBcxABA--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://upload.wikimedia.org/math/5/d/4/5d4fd80761afb572185565cf4b0ad4da.png

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[匿名]

2015-04-29 9:14 am

P1. Both have the same probability of drawing the red ball. The sample space, n, and the event space, r, do not change with replacement. This implies draw by first person and draw by second person are independent. They are independent events.

2015-04-29 01:37:53 補充：
P2. Have you learned convolution? If yes, it won't be hard to find P(X1+X2+...+Xn> 1). If no, distribution of sum of uniformly distributed random variables is the Irvin-Hall distribution. Here's the link for reference: http://www.math.uah.edu/stat/special/IrwinHall.html

2015-04-29 03:09:12 補充：
However, you'll only need cdf of Irvin-Hall. If you have any questions regarding the formula, feel free to ask.

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