p******5
发帖数: 138 | 1 If the first person picks a number randomly from 1 to 100, and the second
person can only guess once, of course he should guess 100 (100 has the same
probability as other numbers to appear and he will get more reward), and the
expected reward is 1/100 * 100 = 1$.
So the second one would like to pay at most 1$ to play this game. |
|
t********s
发帖数: 54 | 2 Why would you consider the strategy of picking number i with probability
proportionaly to 1/i?
1
the |
|
a*****h
发帖数: 484 | 3 Yeah. Well, Blook gave a nice explanation already--it is more likely to be a
game theory problem than a probability one. Sorry for the misleading title.
.. |
|
x*a
发帖数: 48 | 4 schiele, very elegant math and leads to the same results. Kudos.
However, I believe Lagrange does not apply here since
1. It's not a joint optimization. For 2, all you can control is {q_i},
likewise {p_i} for 1.
2. Hypothetically consider a joint optimization, what does this p_i~1/i mean
really? It's probably just a saddle point (鞍点), not one of its local
extrema (it's not quadratic). In fact, the maximum is when p100=q100=1 and
minimum is whenever all (p_i,q_i) pairs have at least one zero valu... 阅读全帖 |
|
k*******a
发帖数: 772 | 5 I think it would be $1
As second person, he can bet 100 all the time, and the probability he can
win is 1/100, so expected return is 100*1/100=1
if he guesses others, expected would be k/100<1
so, he should always bet on 100
The issue here is: first person is randomly pick, but second person don't
have to randomly guess |
|
b**********7
发帖数: 389 | 6 刚面过的一道题，我当时没有彻底回答出来，想跟大家讨论下。
题目是这样的。
假设
G(T)：riskfree zero coupon bond price
B(T)：risky zero coupon bond price
X(T)：survival probablity
我们知道 X(T） = B(T)/G(T)。 然后把X(T) vs maturity（T)的曲线画出来后，发现
这不是一条平滑的衰减曲线，而是在中间部分有一个突起的曲线（对应中长期maturity
）。
问这样的情况是不是存在arbitrage？如果是，在什么情况下是arbitrage？ |
|
n*******e
发帖数: 107 | 7 最开始的想法：
*************************************************************************
窃以为：
这条曲线不可能上升的，因为是对应了cumulative survival probability
如果突起说明那一段的B(T)被over price了，应该在相应的T long G short B
*************************************************************************
想了想又觉得不对，刚才没考虑recovery的问题。
如果市场有充足的信息，证明那一段时间B的issuer即使default也有很高的recovery
rate，那么这个price就是合理的。比如capital structure的突变，equity piece变得
很大，debt piece变得很小。
所以结论应该是：你不知道能不能arbitrage，你的信息不完整，需要对B的issuer进行
单独分析。
maturity |
|
l******i
发帖数: 1404 | 8 1.
P(两个都是男孩|至少有一个男孩)
= P(两个都是男孩) / P(两个孩子里至少有一个男孩)
= (1/2) * (1/2) / (3/4)
= 1/3.
2.
P(两个都是女孩|老大是女孩)
= P(两个都是女孩) / P(老大是女孩)
= (1/2) * (1/2) / (1/2)
= 1/2.
3.
P(三个都是女孩|老三是女孩)
= P(三个都是女孩) / P(老三是女孩)
= (1/2) * (1/2) * (1/2) / (1/2)
= 1/4.
首先感谢楼主贡献，
如果可以的话，希望楼主最好能在帖子标题里加上问题的类别和关键词，
例如该帖名字可为：【Probability Problem】面试题
这样方便我们工作人员整理，谢谢啦。
我已经把标题改了。 |
|
l******i
发帖数: 1404 | 9 首先感谢楼主贡献，
如果可以的话，希望楼主最好能在帖子标题里加上问题的类别和关键词，
例如该帖名字可为：【Probability Problem】一道面试题
这样方便我们工作人员整理，谢谢啦。
我已经把标题改了。
关于楼主给的题目本身：
If X1 and X2 are two independent standard normal random variables,
then Z = X1·X2 follows the "product-normal" distribution
with density function fZ(z) = K0(|z|)/π,
where K0 is the modified Bessel function of the second kind.
See details here:
http://mathworld.wolfram.com/NormalProductDistribution.html |
|
k*****y
发帖数: 744 | 10 Probably either the region of interest or the complement is a cone.
记得 |
|
c****d
发帖数: 13 | 11 The transformation suggested by lichenni is useful. The answer is 35/36.
Here is the verification from Mathematica
Integrate[
Boole[x + 2 y + 3 z <= 22], {x, 2, 4}, {y, 2, 4}, {z, 2, 4}]/8
RegionPlot3D[x + 2 y + 3 z <= 10, {x, 0, 2}, {y, 0, 2}, {z, 0, 2}]
If we want to calculate by pencil, we will find that the plane the z=2 at
the pints
(2,1,2), (0, 2,2), (2, 2, 4/3).
The small tetra that is above the plane is the above three points and (2,2,2
). The volume is 1/3 * (2-4/3) * (1/2 * 1 *2) =2/... 阅读全帖 |
|
n******t
发帖数: 189 | 12 we try to toss a fair die, let Sn is the sum of the first n tosses result,
what is the probability that Sn is divisible by 13 as n goes to infinity? |
|
l******i
发帖数: 1404 | 13 首先感谢楼主贡献，
如果可以的话，希望楼主最好能在帖子标题里加上问题的类别和关键词，
例如该帖名字可为：【Probability】a problem
这样方便我们工作人员整理，谢谢啦。
我已经把标题改了。 |
|
n******t
发帖数: 189 | 14 I got the idea. Write the MC tran matrix and get the stationary probability.
.. |
|
d********t
发帖数: 9628 | 15 I thought about that. But I doubt if that's the interviewer's intention
since the matrix could be big and multiplying it to get stationary may not
be easy.
probability. |
|
d****d
发帖数: 2919 | 16 这个可不是change of variable 的题吧。
这个是order statistics，绿书probablity那章最后有。
思路是先求cdf再求导就成了pdf了。 |
|
c**********e
发帖数: 2007 | 17 【Probability】some MS written test questions
by xiaoyuesixi (bigredbear),
5. find the coefficients before df/dx in the B-S equation for the price of
an option which pays off max(S_T^2-K,0) where S_T is the usual stock
price.
( my answer is (r+sigma^2/2)S^2).
I do not think the answer is correct. Anybody has any comment? |
|
h*****u
发帖数: 204 | 18 On page 228 Shreve II:
Definition 5.4.3 A probability measure Q is said to be risk neutral if
(i) Q is equivalent to P.
(ii) Under Q, the discounted stock price is a martingale.
My question: He uses the discount stock price is a martingale,
why not the discount portfolio is a martingale?
My comment: From my experience, we usually use the risk neutral measure to
compute the option price.(?? Is this right?)
But in section 5.5 dividend-paying stocks,(page234-237) he said under the
risk neutral mea... 阅读全帖 |
|
a****t
发帖数: 720 | 19 totally you have (n choose m) way to pick up m numbers, each way has same
probability, and notice each number i from 1 to n in this (n choose m) ways
appears m times, so expectation is
(1+n)*n*m/(n choose m)=m(n+1)/2
var can be calculated in same way. |
|
c**********e
发帖数: 2007 | 20 With 50% probability, the ball is put in one of the 8 draws. |
|
k***t
发帖数: 33 | 21 Conditional probability gives 1/9, but suppose we conduct the experiment one
million times, and each time the opened 7 drawers are empty, what is the
expected number
of times that one finds the ball in the 8th drawer? Confused. |
|
m****r
发帖数: 141 | 22 they are similar, but the difference is :
In green book , there is 2/3 probability to choose a door w/o price.
So, switching is better than not.
Here, we still have 9 possible choices to make in the remaining 10 seats. |
|
h**********o
发帖数: 37 | 23 70% students choose class A
80%students choose class B
85% students choose class C
90% students choose class D
what is the minimum probability for students choose all ABCD classes.
I think it is 70%+80%-1=50%.
Am I right? |
|
d*******r
发帖数: 7 | 24 Good point. So we should also include a series of hypergeometric
probabilities. Suppose the nth trial is a tail, we need to lose 49 in the
previous n-1 trials. so n has to be 50,53,56,59...,98(every head counteract
2 tails). Just an idea, but it's doable.The other part was discussed. |
|
l******i
发帖数: 1404 | 25 Suppose the coin is fair. I gain one on a head and lose one on a tail. I
quit when my position is +1.
What's the probability that the game terminates?
What's my expected winnings when the game ends?
Please explain in details. |
|
l******i
发帖数: 1404 | 26 这是个很好的解释，但是
Probability that the game terminates = 1，这有什么简单解释吗？
。 |
|
B*********r
发帖数: 62 | 27 X ~ N(0,1), Y ~ N(0,1), X and Y are independent; what is conditional
probability P( X>0 | X+Y>0 )? |
|
m*****e
发帖数: 207 | 28
If no calculator is allowed, then use the 68-95-99.7 rule.
1.3435 is between 1 and 2 sd, so the corresponding quantile
shd be between 84% and 97.5%.
hence the probability is between .025 and .16 QED |
|
n*n
发帖数: 1378 | 29 A prisoner is trapped in a cell containing 3 doors. The
first door leads to a tunnel that returns him to his cell
after 2 days travel. The second to a tunnel that returns him
to his cell after 4 days travel. The third door leads to
freedom after 1 day of travel. Assume that the prisoner
selects doors 1,2, and 3 with probabilities 0.5, 0.3, and
0.2. (Perhaps they drug him so that he does not remember
which door he previoisly selected.) What is the expected
amount of time before the prisoner reach |
|
b*****e
发帖数: 474 | 30 Assuming P(n,k) is the probability that there are 2k+1 white balls
at the n'th step, then the recursive relation is:
P(n,k) = (2n-2k-1)/(2n)*P(n-1,k) + (2k-1)/(2n)*P(n-1,k-1)
Let P(n,k) = f(n,k)/D(n,k), where D(n,k)=(2n)!!/((2k-1)!!*(2n-2k-1)!!).
Here !! is double-factorial, i.e., m!! = m*(m-2)*(m-4)*(m-6)..., thus
f(n,k) = f(n-1,k) + f(n-1,k-1). We can easily prove (by induction) that
f(n,k) = q * C(n,k), where q is a constant, and C(n,k) is
the combinatorial number = n!/(k!*(n-k)!).
(recall C( |
|
d*z
发帖数: 150 | 31 I found a formula without subtract, but the calculation may
be time costing.
Let
U(n,1)=1 when n>=1
U(m,n)=0 when m
U(n,n)=1 when n>=1
and
U(m,n)=n U(m-1,n)+U(m-1,n-1) when m>=n>=2.
Then the probability will be
U(m,n)n!/n^m. |
|
|
f**d
发帖数: 768 | 33 刚才在网上查找，有一篇文章，讲设计计算机玩国际象棋算法时谈到possibility
function 和probability function 之间的关系，请各位大侠们来看他提到的定义和
相互关系可以接受吗？
(Lecture Notes in Computer Science
Publisher: Springer-Verlag Heidelberg
ISSN: 0302-9743
Volume: Volume 2199 / 2001
Date: January 2001
Page: 75 )
A Generalized Uncertainty Function and Fuzzy Modeling
Arkady Bolotin
....
The possibility function q is that mathematical entity which allows us
to determinethe possible results of an interaction between an observed
system and a measuring |
|
s**********2
发帖数: 61 | 34 Thanks for your reply. I understand the conditional probability density part
now. I am not sure that I understand the second line. Could you elaborate?
I was able to duplicate the results of getting 1/y, but I am not sure that I
am getting the right expectation value for x^3, I am currently getting (y^3
)/4, am I doing it properly? Thank you very much. |
|
b****y
发帖数: 257 | 35 Dear Da niu,
I am trying to compare the performance of several algorithms that has
different succ rates and use
different number of resources. For example, algo A has overall succ rate of
60% while using 10 resources,
algo B has overal succ rate of 85% while using 30 resources. It's hard to
compare them since algo A has
less succ rate but use less resources. I am thinking of normalize their
success rate to the same(i.e. 95%) by
assuming each run will have the same succ probability, i.e each run |
|
b*******n
发帖数: 61 | 36 Just consider any one number in the array. The probability that this number
will be chosen at least one time in n times is 1-(29/30)**n.
further? |
|
h**h
发帖数: 488 | 37 求solution manual of Introduction to Probability Models, 9th Edition, by
Sheldon M. Ross
Some exercise problems are too hard, hope to get some help with the manual. |
|
j*****e
发帖数: 182 | 38 Don't do this. Once your instructor finds this out, you will face severe
consequence. I teach in a university and I am not kidding.
If you get stucked by some steps, just ask your instructor for hint. Show
him/her where you cann't get through. You will get at least partial point,
and probably a good impression that you care about your work.
It is very important to be honest person in the USA. |
|
h**h
发帖数: 488 | 39 The course I am taking does not require any homework turn in. Last year,
another instructor even did not use textbook exercises for homework,
considering exercises were too high level for students in our department for
a low level course.
This book is a classic probability one and can be used to teach various
subjects in many fields. For our level, we go really fast which is the
reason my professor does not require to do homework at all. For some
chapters he already gave us the solutions. My con |
|
z*********o
发帖数: 541 | 40 在哪些条件下使用baye's theorem,在哪种条件下使用coditional probability？谢谢 |
|
W**********E
发帖数: 242 | 41 要用C写算法，用到统计分布。谁知道哪里能找到probability function package? 最
好有noncentral t, f, chi的分布。好像R 里的概率分布是调用c 程序，不知道那里能
找到。
多谢！ |
|
o******6
发帖数: 538 | 42 ☆─────────────────────────────────────☆
szbill (风) 于 (Sun May 11 20:19:11 2008) 提到:
toss a coin 100 times, what's the probability at least 60 of them are heads?
☆─────────────────────────────────────☆
redvalley (cabbage) 于 (Sun May 11 20:47:40 2008) 提到:
0.0176
heads?
☆─────────────────────────────────────☆
szbill (风) 于 (Mon May 12 00:15:38 2008) 提到:
Why?????
☆─────────────────────────────────────☆
drburnie (专门爆料) 于 (Mon May 12 01:27:46 2008) 提到:
是0.0284
☆──────────────────── |
|
a*****n
发帖数: 5158 | 43 有一组数据
X(i),error_X(i), Y(i),error_Y(i), coefficient of error_X(i) and error_Y(i)
要做least square linear regression,assume error is norm distribution
怎么计算probability of fit? |
|
m********h
发帖数: 60 | 44 对于bivariate normal distribution,我们可以用 probbnrm.
但是想计算 probability of 3-dimension multivariate normal distribution，不知
道SAS里面有没有function可以用的？或者有什么办法可以计算的用SAS。
多谢！ |
|
|
ki
发帖数: 25 | 46 请推荐一本 probability 的中级(math advanced undergrad - master level)教材 和
一本 statistics 的中级 (stat master level) 教材.
谢谢。 |
|
W**********E
发帖数: 242 | 47 这里有谁知道R里PROBABILITY DISTRIBUTION FUNCTION的C源程序怎么下？ 原来下过
，但不记得了。
thanks, |
|
s***7
发帖数: 506 | 48 有rician噪声的信号，probability distribution 函数里面的
sigma^2,是variance，这个量怎么求，用实验值还是无噪声值，
谢谢回复。 |
|
b*****n
发帖数: 685 | 49 I think it should be the emission probability of the last state.
Maybe it doesn't matter because you don't know the last hidden state. |
|
a***r
发帖数: 420 | 50 搞明白了，是beta定义不同
如果是beta t(i)=P(Ot+1,Ot+2,...OT|qt=Si,λ)
那betaT（i)=p（OT+1|qT=Si,λ）
其实已经没有further observation了，或者理解成，是啥都可以，故1
有的地方beta定义的是
beta t(i)=P(Ot,Ot+1,...OT|qt=Si,λ)
这个时候betaT(i)=p（OT|qT=Si,λ）,即emission probability，对应induction也稍
不同
解出来答案应该是一样的
小问题，不过还是恍然大悟了一下
顺便觉得要补数学啊补数学。。。sigh。。。 |
|
