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全部话题 - 话题: choose
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f********e
发帖数: 1984
1
http://greenopolis.com/myopolis/blogs/aresende/what-you-should-
Things You can Buy Safely (Non-organic)
Fruit
Avocado
Their thick skins that protect the fruit from pesticide build-up.
How to Buy it: You want an avocado that is slightly unripe and is firm tot
he squeeze, they will ripen in a few days of sitting on your kitchen counter
. Store at room temperature. Even though you won't be using the skin of the
avocado, be sure to rinse it anyway before you open it up.
Bananas
The banana peel isn't... 阅读全帖
w*******e
发帖数: 17
2
来自主题: TAX版 - 第六年F1报税8843表的问题
刚才上turbotax的论坛看了一下,有人解答了这个问题,说是先把5000块当成额外收入
报上去,然后再填treaty减去5000.我复制下来贴在这里
You will enter the 1042-S income under other earned income (or scholarship
income if it is for a scholarship grant)and you will enter the amount of the
treaty exemption (if any available) as a negative amount under other
miscellaneous income. You may also need to attach Form 8833 to your tax
return. (Attaching this form will require that you mail in your return. You
will need to select - file by mail under the file tab.)... 阅读全帖

发帖数: 1
3
http://www.ft.com/content/19d90308-6858-11ea-a3c9-1fe6fedcca75
Yuval Noah Harari: the world after coronavirus | Free to read
This storm will pass. But the choices we make now could change our lives for
years to come
Yuval Noah Harari MARCH 20 2020
Be the first to know about every new Coronavirus story
Humankind is now facing a global crisis. Perhaps the biggest crisis of our
generation. The decisions people and governments take in the next few weeks
will probably shape the world for years to com... 阅读全帖
p****r
发帖数: 9164
4
we can assume most ppl are gambling with limited BR. We should always think
about risk averse factor when making decision, even at poker table ie, EV
is NOT the only factor that we should consider. This is also fun part of
poker,IMO.

In Bill chen's book, it gave a simple example. If we are given a
chance to choose two following options. We use coin flip as gambling tool.
Chance are strictly 50/50
1. We keep 1 million$ without any risk/gambling.
2. We gamble 1 time coin flip,... 阅读全帖
w*s
发帖数: 7227
5
Hi 大牛们,
i downloaded AdventureWorks2012_Data.mdf,
i can open it using sql server 2012 express.
Now i'm following the book trying to create a c# project connect to it,
(the book uses NorthWind db file, i cannot open it as it's not for sql 2012)
at step 9, i choosed my db file, i click "ok", but nothing happens other
than hearing a bell.
Any help appreciated !
1. Create a new console application project called BegVCSharp_24_1_
FirstLINQtoDatabaseQuery in the
directory C:BegVCSharpChapter24.
2. Pre... 阅读全帖
m****n
发帖数: 45
6
来自主题: Mathematics版 - Puzzle 1.
Suppose there are 2n numbers x_1,...,x_{2n}.
If x_1+x_3+...+x_{2n-1}>= x_2+x_4+...+x_{2n}
Player A should choose x_1.
Because after you choose x_1, B can only choose a number with even subscript.
After B choose a number, you can choose a number with odd subscript again and
B can only choose a number with even subscript.
A keeps choosing numbers with odd subscript and B can only choose numbers with
even subscript.
At the end, A would not lose.
If x_1+...+x_{2n-1} < x_2+...+x_{2n}, Player A should
d*********i
发帖数: 19
7

into
I just thought about half of the problem.
Since balls with the same color cannot be in the same bin, consider throwing
the balls as choose 5 bins out of 15 for each color and these events are
independents.
∴ the total number of ways to put the 60 balls into 15 bins are (15 choose
5)^12
Then for each bin, P(it contains 0 ball)= (14 choose 5)^12 / (15 choose 5)^
12
P(1)= (12 choose 1)*(14 choose 4)* (14 choose 5)^11 / (15 choose 5)^12
∴ the probability of one bin containing at least 2 balls
q********u
发帖数: 17
8
You will receive 50k points after FIRST purchase and 50k on first card
anniversary.
The Annual fee is $75 that is NOT waived the first year. IMO it's worth
paying $75 to get 100k Avios points with NO minimum spend.
here's what you do.
use Chrome INGONITO mode or Firefox PRIVATE BROWSING. You HAVE to use either
of these modes. It has something to do with the cookies, that prevents the
offer from popping up.
You go to britishairways.com and Choose the US site.
Then you Choose a ONE WAY trip betwee... 阅读全帖
t*****r
发帖数: 4431
9
来自主题: Seattle版 - 黄石公园11天10夜游线路参考
黄石公园,作为全美第一个国家公园,它的美是无与伦比的。至于游览多长时间为好,
根据自己的时间和兴趣,要想每个景点看一遍,至少要在里面玩三天。大部分旅行社的
线路安排都是一整天,走马观花,在几个著名景点前拍照留念,到此一游。每年的黄石
公园线路总是最受欢迎的,今年8月份的线路提前一个月就定满了。西雅图出发5天大巴
团,比起飞到盐湖城、洛杉矶、拉斯维加斯来参团有利有弊。好处是省心,从家门口出
发,5天后返回,不需要经过飞行、接机送机的麻烦,费用低很多;缺点就是,坐车时
间长。好在沿途停留的景点不少。
下面这个线路,是西雅图一帮爱好旅游的老外定的线路,大部分是单身,参团并交友,
线路比我们的长一倍,安排了更多的游玩项目。当然,他们的费用是我们的6倍!线路
供自驾游的朋友参考。
黄石公园11日游线路
费用:
单人 $3,524/人 (正常价格 $3,775)
双人: $2,549/人 (正常价格$2,709)
三人: $2,224/人 (正常价格$2,354)
四人: $2,061/人 (正常价格$2,177)
(买十送一,也可以分期付款)
费用全包:
全程豪华旅游车
宾馆
三餐(含税和小费)... 阅读全帖
w****1
发帖数: 4931
10
来自主题: Running版 - successfully cut down some bodyweight
It's not so much about the exact food but about the principle of eating. If
you get to choose between a deli
sandwich and a cheese burger, choose the sandwich with pumpernickel bread.
When you eat a salad, don't
use dressing. when you get to choose between white rice and brown rice,
choose the brown rice. between
white and dark bread, choose the dark bread. between fried chicken and
grilled chicken, choose the grilled
chicken. between water and coke, choose water. skip that dessert and skip
the
c*******g
发帖数: 12
11
来自主题: Ski版 - 【推荐】如何挑选滑雪板
看到一篇文章不错,给大家推荐一下
今天入手了Sapient 的PNB1,打算这个season开始练park了。这里有没有经验丰富的玩
家大家认识一下啊。
http://www.rei.com/expertadvice/articles/snowboard.html
Snowboard boots should be your first acquisition when assembling a board-
boots-binding setup. You want your boots to fit comfortably so you can move
on to bindings and create a great match. Boots, more than a board, are where
you want to splurge a little if you can afford to do so.
The snowboard boots you select should be well matched to your usual riding
style an... 阅读全帖
g********5
发帖数: 62
12
来自主题: Mathematics版 - statistics 入门问题
You should ask this question in Statistics board.
I do not understand your second question. Solution to 1th question is:
Prob(all 39# are zero)
= (39 choose 20) / { (20 choose 20) + (21 choose 20) + ...+ (39 choose 20) }
= (39 choose 20) / (40 choose 21)
= 21/40
where (n choose k)= n!/{ k!(n-k)! }
t*****r
发帖数: 1765
13
(纽约州),这就是你在
国内的认证机构会收到这样一份表格,以前主要是给学校填的,如下,英文还看不明白
的,中文翻译在最下面。本文仅供参考交流,如有律师中介协助办理,以律师为准。
Verification of Academic Record
CGFNS P.O. Box 8628,Philadelphia PA 19104-8628 USA Telephone(215)349-8767
Fax(215)349-0026 Email:e****[email protected]
Applicant Name:____1____ Date of Birth:______2_______
Type of Program:______3___ Years of Education Required for Admission:______4
____
Name of Degree/Diploma Awarded:________________5____________________________
(Please print title of degree/diploma in native lang... 阅读全帖
g******2
发帖数: 234
14
来自主题: Quant版 - 又见coin 难题
The following R code should give you the right probability for P(N_group = k
| n flips).
prob <- function(k, n) {
if (k > 1) {
if (k%%2 == 0) {
nums <- (k/2) : (n-k/2)
p <- sum(sapply(nums, function(x)
choose(2,1)*choose(max(x,n-x)-1, k/2-1) *
choose(min(x,n-x)-1, k/2-1) * 0.6^(n-x) *0.4^x))
return(p)
} else {
nums <- floor(k/2) : ceiling(n-k/2)
p <- sum(sapply(nums, function(x)
choose(max(x,n-x)-1, floor(k/2)) ... 阅读全帖

发帖数: 1
15
来自主题: Quant版 - 又见coin 难题
I like R so I checked your R code.
could you double check your R code? using k=n=10,
> prob <- function(k, n) {
+ if (k > 1) {
+ if (k%%2 == 0) {
+ nums <- (k/2) : (n-k/2)
+ p <- sum(sapply(nums, function(x)
+ choose(2,1)*choose(max(x,n-x)-1, k/2-1) *
+ choose(min(x,n-x)-1, k/2-1) * 0.6^(n-x) *0.4^x))
+ return(p)
+ } else {
+ nums <- floor(k/2) : ceiling(n-k/2)
+ p <- sum(sapply(nums, function(x)
+ choose(max(x,n-x)-1, floor(k/2))... 阅读全帖
W**********E
发帖数: 242
16
来自主题: Statistics版 - Faster Random Sampling with Replacement
不错,有个问题
如果从N个样本里取N个,那么number of hits 的PMF是:
P(Z=x)=(n,x)*(1/N)*(1-1/N)^(N-x)
根据这个PMF,expected number of hits 和你的output差不多:
> (1/N)*(1-1/N)^(N-1)*choose(N,1)*N
[1] 3678795
> (1/N)^2*(1-1/N)^(N-2)*choose(N,2)*N
[1] 1839397
> (1/N)^3*(1-1/N)^(N-3)*choose(N,3)*N
[1] 613132.4
> (1/N)^4*(1-1/N)^(N-4)*choose(N,4)*N
[1] 153283.1
> (1/N)^5*(1-1/N)^(N-5)*choose(N,5)*N
[1] 30656.6
....
当N->inf, 上面的PMF是可以渐进到一个Poisson(lambda=1)
比如Z=1,
(1/N)*(1-1/N)^(N-1)*choose(N,1)
=(1-1/N)^(N-1)
->(1-1/N)^N
->e^-1
比如Z=2,
(... 阅读全帖
P*******0
发帖数: 226
17
来自主题: Statistics版 - 药厂面试准备资料
Behavior questions:
-------------------------------------
Questions Asked By Employers
• What are your long range and short range goals and objectives,
when and why did you establish these goals and how are you preparing
yourself to achieve them?
• What specific goals, other than those related to your occupation,
have you established for yourself?
• What do you see yourself doing five years from now?
• What do you expect to be earning in five years?
• ... 阅读全帖
f**********4
发帖数: 2617
18
来自主题: History版 - 谁打过十字军之王?
In general, the laws and techs in CK are not very important, at least for me.
To choose which kind of inheritance law depends on which child you would
like to be the next ruler. Primogeniture passes all the power to the eldest
son and is the most popular law in Europe. But if your eldest son happens to
be an idiot, and your second son is a genius, you can choose Consanguinity,
which awards the "strongest" son everything. Then you can artificially
makes your 2nd son the "strongest" by awarding hi... 阅读全帖
s*****n
发帖数: 839
19
我的建议在这里:
About Diao Yu Island.
Proposal:
Solution attempted:
Solution A: boundary line as Japan suggested, but 1:9 (Japan: China) the oil
well number ratio
Solution B: boundary line as China suggested, but 1:9 (China: Japan) the oil
well number ratio
Ask China and Japan, which option they choose.
If both choose A or B, agreement achieved.
If Japan choose B, China choose A(both prefer oil over boundary)===>the
ratio should drop to 1:8
If Japan choose A, China choose B(both prefer bounday over oil... 阅读全帖
m**c
发帖数: 7349
20
Both predicaments were a consequence of the macroeconomic policy trilemma,
also called the impossible trinity. It says a country must choose between
free capital mobility, exchange-rate management and an independent monetary
policy. Only two of the three are possibleBoth predicaments were a
consequence of the macroeconomic policy trilemma, also called the impossible
trinity. It says a country must choose between free capital mobility,
exchange-rate management and an independent monetary policy.
... 阅读全帖
s*****n
发帖数: 839
21
我的建议在这里:
About Diao Yu Island.
Proposal:
Solution attempted:
Solution A: boundary line as Japan suggested, but 1:9 (Japan: China) the oil
well number ratio
Solution B: boundary line as China suggested, but 1:9 (China: Japan) the oil
well number ratio
Ask China and Japan, which option they choose.
If both choose A or B, agreement achieved.
If Japan choose B, China choose A(both prefer oil over boundary)===>the
ratio should drop to 1:8
If Japan choose A, China choose B(both prefer bounday over oil... 阅读全帖
s*****n
发帖数: 839
22
来自主题: RisingChina版 - 钓鱼岛问题公平解决具体方案建议
我的建议在这里:
About Diao Yu Island.
Proposal:
Solution attempted:
Solution A: boundary line as Japan suggested, but 1:9 (Japan: China) the oil
well number ratio
Solution B: boundary line as China suggested, but 1:9 (China: Japan) the oil
well number ratio
Ask China and Japan, which option they choose.
If both choose A or B, agreement achieved.
If Japan choose B, China choose A(both prefer oil over boundary)===>the
ratio should drop to 1:8
If Japan choose A, China choose B(both prefer bounday over oil... 阅读全帖
g********2
发帖数: 6571
23
First lady Michelle Obama has wrapped up her six-day “Let Girls Learn”
tour of Liberia, Morocco and Spain. Together with her mother Marian and two
daughters Sasha and Malia, the FLOTUS, under the guise of promoting access
to education for 62 million girls worldwide, embarked on a multimillion-
dollar excursion where she ate great food, wore great clothes, hung out with
celebrities, and spent $600,000 for one night in Marrakesh.
In Madrid, while speaking to schoolgirls about equality, Michelle d... 阅读全帖
W***n
发帖数: 11530
24
The Real Cost of Your Car’s Cheap Factory Air Filter
by Timothy Zahl on December 03, 2015
Air Filters Selection
In today's world, saving money wherever possible has become essential. But
it's important not to lose sight of the fact that, sometimes, a product that
costs more up front will save you more money over time. In our business, we
've seen far too many consumers judge products solely on the basis of their
initial cost, completely neglecting any long-term economy and benefits. When
it come... 阅读全帖

发帖数: 1
25
来自主题: Faculty版 - Jan's lab : 这里有弟子么?

Download pdf published by SfN (Chapter from 'The History of Neuroscience in
Autobiography, Volume 8' edited by Larry R. Squire)
Yuh-Nung Jan's CV
Lily Jan's CV
Yuh-Nung Jan and Lily Jan
Birth
Family History and Growing Up
National Taiwan University
The Hiking Trip to Shitou in the Spring of 1967
Graduate School Application
Graduate Study at Caltech (1968锟974)
Seymour Benzer Lab (1974锟977)
Steve Kuffler锟絪 Lab at H... 阅读全帖
f****4
发帖数: 1359
26
找到一个对的O(N)的解法
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=ri
This is a pretty good puzzle. You can actually find the cutoff and a
description of exactly which pairs are in the solution in less than O(N)
time, but outputting all the solutions takes O(N) time, so it doesn't help
you overall. This won't be much of a hint, but finding the cutoff point can
be done in O(sqrt(N)*log2N) time. Forgive me for not writing code, but this
gets pretty nitty-gritty in spots.
I think of the pro... 阅读全帖
f****4
发帖数: 1359
27
找到一个对的O(N)的解法
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=ri
This is a pretty good puzzle. You can actually find the cutoff and a
description of exactly which pairs are in the solution in less than O(N)
time, but outputting all the solutions takes O(N) time, so it doesn't help
you overall. This won't be much of a hint, but finding the cutoff point can
be done in O(sqrt(N)*log2N) time. Forgive me for not writing code, but this
gets pretty nitty-gritty in spots.
I think of the pro... 阅读全帖
w*******n
发帖数: 150
28
来自主题: Stock版 - IB账户申请
上面的明白了,又让我填投资经验
Stocks 0 1 2 3 4 5 6 - 10 > 10 0 1 - 10 11 - 25 26 - 50 51 - 100 > 100
0 Choose One Extensive Good Limited
Stocks To qualify to trade Stocks in a Cash account, your Investment
Objectives must include one of the following: Income, Growth, Trading
Profits, Speculation or Hedging.
Bonds 0 1 2 3 4 5 6 - 10 > 10 0 1 - 10 11 - 25 26 - 50 51 - 100 > 100
0 Choose One Extensive Good Limited
Bonds To qualify to trade Bonds in a Cash account, your Investment
Object... 阅读全帖
w*******n
发帖数: 150
29
来自主题: Stock版 - IB账户申请
上面的明白了,又让我填投资经验
Stocks 0 1 2 3 4 5 6 - 10 > 10 0 1 - 10 11 - 25 26 - 50 51 - 100 > 100
0 Choose One Extensive Good Limited
Stocks To qualify to trade Stocks in a Cash account, your Investment
Objectives must include one of the following: Income, Growth, Trading
Profits, Speculation or Hedging.
Bonds 0 1 2 3 4 5 6 - 10 > 10 0 1 - 10 11 - 25 26 - 50 51 - 100 > 100
0 Choose One Extensive Good Limited
Bonds To qualify to trade Bonds in a Cash account, your Investment
Object... 阅读全帖
w*******n
发帖数: 150
30
来自主题: Stock版 - IB账户申请
上面的明白了,又让我填投资经验
Stocks 0 1 2 3 4 5 6 - 10 > 10 0 1 - 10 11 - 25 26 - 50 51 - 100 > 100
0 Choose One Extensive Good Limited
Stocks To qualify to trade Stocks in a Cash account, your Investment
Objectives must include one of the following: Income, Growth, Trading
Profits, Speculation or Hedging.
Bonds 0 1 2 3 4 5 6 - 10 > 10 0 1 - 10 11 - 25 26 - 50 51 - 100 > 100
0 Choose One Extensive Good Limited
Bonds To qualify to trade Bonds in a Cash account, your Investment
Object... 阅读全帖
u*1
发帖数: 907
31
来自主题: GunsAndGears版 - CCW的手枪的一些问题
In 254 shooters who have CCW, 221 carry handguns with 6 common calibers:
104 choose 9mm, 47.06%
52 choose .45 ACP, 23.53%
26 choose .40 S&W, 11.76%
26 choose .38 Special, 11.76%
10 choose .38 ACP, 4.52%
3 choose .357 Mag, 1.36%
--IDPA 2012 equipment survey

sub
r********m
发帖数: 593
32
来自主题: Exchange版 - 转转小样---A to Z
这楼贴各种杂牌的东东.
带***的请从下楼里的"免费赠品"里选.
===AHAVA=== 图1
除非特别说明,小样为管装
***Choose one sample free with any AHAVA purchase***
Deadsea osmoter concentrate 精华, bottle
131230026E
Size 5mL
Value 12.00
Price 1.00
Deadsea plants firming body cream
130402010
Size 40mL
Price 1.00
Deadsea water mineral body exfoliator
131201006
Size 40mL
Price 1.00
Deadsea water mineral hand cream
130102023
Size 20mL
Price 1.00
**********************************************************... 阅读全帖
c******o
发帖数: 1184
33
来自主题: WaterWorld版 - Zakaria: Will China stay on course?
Will China stay on course?
By Fareed Zakaria, CNN
Events in the Middle East and North Africa are of historic importance, but
the even bigger, long-term story is the rise of China. What path will it
choose at home and abroad in the years ahead?
For decades there has been debate at the highest levels of the Chinese
government about how much to modernize politically to ensure growth and
stave off revolution.
It’s notoriously difficult to analyze the inner workings off the Chinese
Communist Party. ... 阅读全帖
J*****3
发帖数: 4298
34
来自主题: TrustInJesus版 - 反基们让我如梦方醒,豁然开朗!
最长的REVIEW
Choosing a holy book is harder than choosing a romance novel. To help you
choose, I will compare this one to another best-seller in this category, the
Quran. These are the two holy books that get the most buzz around here.
Based on all the marketing hype, I expected these two books would be really
different. All readers like one or the other, never both, and they all HATE
the other book. However, these two books turned out to be a lot more similar
than their marketing led me to expect.... 阅读全帖
m****s
发帖数: 18160
35
来自主题: TrustInJesus版 - [合集] 查经贴-使徒行传
☆─────────────────────────────────────☆
Dramaer (不要问我从那里来) 于 (Fri Oct 22 12:02:52 2010, 美东) 提到:
Act 1:1-11 Jesus Taken Up Into Heaven
1In my former book, Theophilus, I wrote about all that Jesus began to do and
to teach 2until the day he was taken up to heaven, after giving
instructions through the Holy Spirit to the apostles he had chosen. 3After
his suffering, he showed himself to these men and gave many convincing
proofs that he was alive. He appeared to them over a period of forty days
... 阅读全帖
Y**u
发帖数: 5466
36
☆─────────────────────────────────────☆
TrueStory (不是幸福的坑不挖) 于 (Wed Nov 23 14:09:26 2011, 美东) 提到:
Carl Jung published a lot after this NDE, and this was one of his two major "creative" illnesses he experienced (suffered or blessed). The other one was the deep depression he experienced after his break-up with Freud (several of Freud's former disci
committed suicide after such break-ups.)
Update: I found a link with the same content, but perhaps it's easier to read than the pure text below:
h... 阅读全帖
z***y
发帖数: 7151
37
来自主题: AC版 - 地主的竞选宣言
May I have a dream, that one day everybody in AC board could
watering at his will, no matter he is white, black, yellow
or green(???)
(hua hua hua, clapping)
May I have a dream, that one day all the top ten is from AC
board。。。。。
众虫虫齐敲水桶, 高呼: go zenny, go zenny, go zenny, go,
go, go go!!!
地主庄严地蹲在主席台上, 向网虫虫挥抓致意。
I need your vote. You choose me, you choose hope, you choose
me, you choose future, and You choose others, you choose the
hell...
呵呵, 后两句记不得是哪部电影里的乐。。。大概是媳拉里的参议
员竞选演说巴。
===============
掐死
wy
发帖数: 14511
38
来自主题: AC版 - [转载] 地主的竞选宣言
【 以下文字转载自 board 讨论区 】
【 原文由 wy 所发表 】
May I have a dream, that one day everybody in AC board could
watering at his will, no matter he is white, black, yellow
or green(???)
(hua hua hua, clapping)
May I have a dream, that one day all the top ten is from AC
board。。。。。
众虫虫齐敲水桶, 高呼: go zenny, go zenny, go zenny, go,
go, go go!!!
地主庄严地蹲在主席台上, 向网虫虫挥抓致意。
I need your vote. You choose me, you choose hope, you choose
me, you choose future, and You choose others, you choose the
hell...
呵呵, 后两句记不得是哪部电影里的乐。。
k*****u
发帖数: 1688
39
hot么?
昨天有个1080的
Dell Home has their Alienware Aurora R7 Desktop on sale starting at $1049.99
- $200 Slickdeals Rebate = $849.99 when you follow the instructions below.
Shipping is free. Thanks RevOne
Available options:
Alienware Aurora R7 Desktop w/ GTX 1070
Under Video Card, choose Nvidia GeForce GTX 1070 8GB (+ $100)
Under Keyboard, choose Alienware Multi-Media Keyboard
Under Mouse, choose Alienware Standard Optical Mouse
Total will be $1049.99 - $200 Slickdeals Rebate = $849.99
Alienware Auro... 阅读全帖
s*****a
发帖数: 353
40
来自主题: Economics版 - 请教多期问题的求解
backward induction是每次做决策的时候考虑别人下面会考虑什么,而forward
induction常常要考虑,如果对方做了一件意料之外的事情,那他在考虑什么
举个例子,two players, 1 chooses A and not A, if he chooses not A, then he
proceed to choosing B, or C, if he chooses A, pay off is 2,0
if he chooses not A, 2 can not tell which he chooses and have the actions of
L and R. payoffs are u(B,L)=3,1, u(B,R)=0,0, u(C,L)=0,0 u(C,R)=1,3
by forward induction, as A dominates C, when 2 is called to play, she
reasons, well, as C is dominated by A, it is impossible that he play
i*****e
发帖数: 68
41
来自主题: Mathematics版 - how to proof
Consider selecting two numbers from 1,2, .., n. There are total (n choose 2)
selections.
The selections can be divided into the following groups:
choose 1, and another number-- total n-1 selections;
choose 2, and another number that is greater than 2 -- n-2 selectins;
choose 3, and another number that is greater than 3 -- n-3 selections;
and so on.
Therefore, (n choose 2) = (n-1)+(n-2)+...+1.
Similarly, you have (n+1 choose 2) = n+(n-1)+...+1 = 1+2+...+n.
Summing up the two equalities you have
(
l*****y
发帖数: 56
42
来自主题: Quant版 - 【Probability】一个题目
E(P)可以用数数的方法做。
每次取m个数,总共有(n choose m)种取法,每种概率一样,都是1/(n choose m), 只
要算出所要的和,再乘以这个概率就可以。
要求所有的和,可以考虑每个数在这个求和中都出现了(n-1 choose m-1)次,所以
E(P)=(n-1 choose m-1)*(1+n)*n/(2*(n choose m))= m*(1+n)/2 .
算Var(P), 只要求出E(P^2), 同样的思路可以算,考虑每个(x1+x2+...xn)^2中有多少
个xi^2 和 xi*xj (i E(P^2)= m/n*[(n+1)(2n^2+1)/6]+ n^2*(n-1)^2*(n+1)*(3n+2)/(n choose m).
H****E
发帖数: 254
43
suppose that prob of score is 1/2
for A. 投3次,中2次或以上。
(1/2)^3 * (3 choose 2) + (1/2)^3 * (3 choose 3) =1/2
for B 投8次,中5次或以上。
(1/2)^8 *((8 choose 5)+(8 choose 6) +(8 choose 7) +(8 choose 8))
=0.36
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