a****a
发帖数: 98 | 1
I think maybe he means the space of 1-dim random variables? this is not a
probability space itself. but it is a hilbert space if you define the inner
product to be covariance, and every hilbert space is a banach space (but
not the other way around) |
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f******h
发帖数: 37 | 2 There are n independent adults who are playing games, each wins with equal
chance that is p. Adults play the game only one time. Then, each adult has a
child who is playing the same game again, but kids win with different
chances which depends on if their parents won.The kid wins with chance b if
his/her parents won, otherwise c, where b>c. Kids are independent on each
other and play the game only one time too. What's the probability
distribution of kid winners?
thanks in advance |
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n***s
发帖数: 1257 | 3 The definition says "{Xn} converges in probability to X iff P(|Xn - X| >= ε
) ---> 0 for every ε > 0". I am wondering if it can be defined without
introducing ε? Specifically, what's the difference between "P(|Xn - X| > ε
) ---> 0 for every ε > 0" and "P(|Xn - X| > 0) ---> 0"? If they are not the
same, as a condition which one is stronger ? Please give some clarification
. Thanks in advance! |
|
m******e
发帖数: 3484 | 4 学mathematical statistics, probability没有real analysis和measure theory的基础
还是比较困难的 |
|
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v*********y
发帖数: 667 | 6 我学的Claculus和自学的Probability里面都没有这些Topics。奇怪。 |
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m******e
发帖数: 3484 | 7 不过这些知识的要点在mathematical statistics和probability里面也会教的
只是如果事先学过理解会比较深刻一些 |
|
v*********y
发帖数: 667 | 8 Thank you very much.
I taught myself Probability and I didn't touch that part, maybe I can find
more advanced book to read. |
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l*********y
发帖数: 5 | 9 这边mathematical statistics or probability的基础要求是real analysis. 我们系
要求修三门real analysis。在美国上过Calculus I II III 就可以上real analysis了
. |
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s****l
发帖数: 41 | 10 toss a coin 100 times, what's the probability at least 60 of them are heads? |
|
E****I
发帖数: 22 | 11 08fall就要上本科了,准备major math, 主要对logic/real analysis/Topology/
probability比较感兴趣(尤其是logic...准备把哲学那边的logic课程也尽量选一些)
可是我实在不知道学这些可以找什么样的工作?master去读生统如何? |
|
d********n
发帖数: 34 | 12 有人用过Rick Durrett的Probability Theory这本书吗？
那里可以找到solution manual?
万分感谢！ |
|
x*******7
发帖数: 409 | 13 Fundamentals of Probability, with Stochastic Processes (3rd Edition)
电子版,最好有中文译本:)免费下载也可以,谢谢 |
|
l******e
发帖数: 470 | 14 看下an introdution to geometric probability, Chapter 2.
里面给了largest piece的分布的公式。推倒挺复杂的。 |
|
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f*****l
发帖数: 82 | 16 【 以下文字转载自 Statistics 讨论区 】
发信人: flywill (flywill), 信区: Statistics
标 题: 问个probability的问题
发信站: BBS 未名空间站 (Sun Feb 14 22:28:15 2010, 美东)
Assume X, Y are iid with mean 0 and variance 1, 如何证明if X+Y, X-Y are inde
pendent, then X, Y are standard normals, thanks! |
|
o**a
发帖数: 86 | 17 【 以下文字转载自 Physics 讨论区 】
发信人: ouba (comfortably numb), 信区: Physics
标 题: a question on probability density
发信站: BBS 未名空间站 (Thu Feb 25 12:26:21 2010, 美东)
Folks, thanks for your time first!
function f = x.cos(a)**2 + y.cos(b)**2 + z.cos(c)**2
I know x > y > z. a, b, c are the angles between a vector and x, y, z axes
of a cartesian coordinate respectively.
If written in nutation and azimuthal angles,
f = x.sin(theta)**2.cos(phi)**2 + y.sin(theta)**2.sin(phi)**2 + z.cos(theta)
**2.
This vector is und |
|
B*********r
发帖数: 62 | 18 X ~ N(0,1), Y ~ N(0,1), X and Y are independent; what is conditional
probability P( X>0 | X+Y>0 )? |
|
o**a
发帖数: 86 | 19 Folks, thanks for your time first!
function f = x.cos(a)**2 + y.cos(b)**2 + z.cos(c)**2
I know x > y > z. a, b, c are the angles between a vector and x, y, z axes
of a cartesian coordinate respectively.
If written in nutation and azimuthal angles,
f = x.sin(theta)**2.cos(phi)**2 + y.sin(theta)**2.sin(phi)**2 + z.cos(theta)
**2.
This vector is undergoing random re-orientation, i.e, the probability
density at (theta, phi) position is 1/(4pi)*sin(theta).
It is easy to see that z <= f <= x. Is th |
|
B*********h
发帖数: 800 | 20 ☆─────────────────────────────────────☆
littletshirt (小仙鹤) 于 (Thu Jan 25 17:44:03 2007) 提到:
ZT:
There are N balls. Out of the N balls, there are M black balls and N-M white
balls. Permutate all balls in a round circle. What is the probability that
at least X black balls are in a row (e.g., WWBBBBBWWWWBWBW....)?
☆─────────────────────────────────────☆
exon (Exon! : )) 于 (Fri Jan 26 15:40:15 2007) 提到:
it is too difficult for me... :(
☆─────────────────────────────────────☆
exon (Exon! |
|
r*****t
发帖数: 286 | 21 ☆─────────────────────────────────────☆
maglion (da木头) 于 (Tue Feb 20 13:51:01 2007) 提到:
A family has 9 children. Suppose any child is equally like to be a boy or a
girl, and the genders of any two children are independent to each other.
Given the information that at least 8 out of these 9 children are boys. What
is the probability that there is a girl in the family?
☆─────────────────────────────────────☆
yogaII (...) 于 (Tue Feb 20 13:52:50 2007) 提到:
1/2
a
What
☆────────────────────── |
|
B*********h
发帖数: 800 | 22 ☆─────────────────────────────────────☆
mjklj (碧云天) 于 (Fri Mar 9 12:45:46 2007) 提到:
Appreciate your suggestion on reading materials (textbooks, notes ..) on
Probability.
☆─────────────────────────────────────☆
mjklj (碧云天) 于 (Fri Mar 9 16:15:36 2007) 提到:
Can anyone recommend a book?
☆─────────────────────────────────────☆
zdg (zdg) 于 (Fri Mar 9 16:37:20 2007) 提到:
the book from Chung is good.
There are 2 books from him I think, one is for under, the other one for grad
level. you |
|
b***k
发帖数: 2673 | 23 A Probability Path by Sidney Resnick
Seems like it is a good preliminary book for Karatzas&Shreve.
People from Cornell U. may find this book classic 'cause the author so
far a professor in orie there. |
|
b***k
发帖数: 2673 | 24 ☆─────────────────────────────────────☆
ifc (ifc) 于 (Thu Oct 11 17:06:15 2007) 提到:
Suppose you are standing on one corner of a cube. You have equal probability
to move to one of the three neighboring corners. What is the expectation
steps from
the corner where you are standing to the furthest corner (diagonal corner)?
☆─────────────────────────────────────☆
JetMax (JetMax) 于 (Thu Oct 11 17:46:09 2007) 提到:
3, similar to a problem discussed a few days ago.
☆──────────────────────────── |
|
w******w
发帖数: 92 | 25 Thank you guys. I also made some computational mistakes. Below is my answer.
Is there any easy way to do it?
We consider B, C and D as one state, and denote it by K.
So P(A->A)=0, P(A->K)=1, P(K->K)=2/3, and P(K->A)=1/3.
The first step the bug must arrive K (since P(A->K)=1).
In order to return A in the 7th step, the bug must be at K in the 6th step
and with
a probability 1/3 to return A (since P(K->A)=1/3). So the problem is changed
to
(1/3)*P(start from K, return to K at the 5th step).
We comp |
|
i***0
发帖数: 37 | 26 why use neutral probability in binomial models
why?
why?
why? |
|
n**x
发帖数: 6 | 27 I guess the probability is 11/1024. The final price is 100 means in the
paths you must have 5 ups and 5 downs, otherwise the final price cannot be
100. Because you start from 100 and can only increase or decrease by 1 one
each day, which means the value of 104 must be arrived at an even number day
(such as day 2, day 4....). And because the maximum is 104, which means the
latest day it can occur is the 6th day, otherwise the final value cannot be
100. And it also means the earliest day it can oc |
|
p********0
发帖数: 186 | 28 in some problem set, prof just assume to be 1/2.
Also if we didnot know the flat term risk free interest rate,
the p = 1/2+ 1/2*v/\sigma*sqrt(t) used in binomial can be considered risk
neutral probablity? |
|
p********0
发帖数: 186 | 29 Assume we are using binomial to derive the short rate lattice
so we can calculate a bond price backward using q=1/2.
The 1/2 is the risk neutral pricing we get, where we get this 1/2,
is the 1/2 risk neutral probability?
===================================================
u 1.3
d 0.9
q 0.5
Short Rate 0.00 1.00 2.00 3.00 4.00 5.00
|
|
b***k
发帖数: 2673 | 30 ☆─────────────────────────────────────☆
smilingxiao (春光无限) 于 (Wed Oct 24 23:10:58 2007) 提到:
They are two probability questions during Quant interview.
Each question needs to calculate the expected number, but I don’t know how
to do it. Looking for the solution.
BTW, Is there any book or paper regarding to solving those kinds of
questions. Thanks
1) Throw a regular coin. If it is head, you get $1, and if it is tail,
you lose $1. Now you have $5. Once you can reach $10, you win the game. I |
|
s****l
发帖数: 41 | 31 toss a coin 100 times, what's the probability at least 60 of them are heads? |
|
A*L
发帖数: 2357 | 32 一个大积分啊
toss a coin 100 times, what's the probability at least 60 of them are heads? |
|
b***k
发帖数: 2673 | 33 ☆─────────────────────────────────────☆
Ithink (牛夫人) 于 (Thu May 1 13:36:50 2008) 提到:
Toss a fair coin until we get a 5H in a row or 2T in a row. What's the probability of getting 5H in a row at the end of the game prior to 2T in a row?
☆─────────────────────────────────────☆
xiaoxiaokuan (小小矿) 于 (Thu May 1 15:08:05 2008) 提到:
=sum((1/2)^i) where i=5,6,7....
=(1/2)^5
☆─────────────────────────────────────☆
Ithink (牛夫人) 于 (Thu May 1 15:20:48 2008) 提到:
emm... not exactly what I wan |
|
b***k
发帖数: 2673 | 34 ☆─────────────────────────────────────☆
littleegg (爱吃茶叶蛋) 于 (Sun Jun 8 14:39:07 2008) 提到:
(1)suppose there are n people in an office, at Christmas, they have a random
gift exchange in which every name is written on scrapes of paper, mixed
around in a hat, then everyone draws a name at random to determine who they
are to get a gift for. What is the probability nobody draws their own name?
(2)what is the expected number of random numbers, uniformly distributed from
0 to 1 needed to the sum t |
|
b***k
发帖数: 2673 | 35 ☆─────────────────────────────────────☆
back20 (back20) 于 (Tue Apr 1 10:33:43 2008) 提到:
Given n nodes in the field(assuming in a large rectangle area) randomly
deployed, and all of them are doing random movement( you can assume speed v,
if needed, and nodes cannot move out of the large rectangle). What is the
probability that there are 0 node, 1 node, 2 nodes,..., n nodes in a small
rectangle(the small rectangle is inside the large rectangle)?
Anyone have ideas for the solution?
☆───────── |
|
b***k
发帖数: 2673 | 36 ☆─────────────────────────────────────☆
quant123 (quant123) 于 (Mon Jul 28 16:44:37 2008) 提到:
Let d(A,B) denote the Euclidean distance between two points A and B.
In the Euclidean plane there are given a circle and a square that are
disjoint but have equal areas. Two points C1 and C2 are randomly chosen in
the circle, and two points S1 and S2 are randomly chosen in the square. Find
the probability that d(C1,C2) > d(S1,S2).
☆─────────────────────────────────────☆
JQKA (新鲜) 于 (Mon Jul 28 2 |
|
g******r
发帖数: 29 | 37 Cinlar, Lecture Notes on Probability
princeton的
想找来看看
多谢 |
|
o********n
发帖数: 100 | 38 请教一道题：
正反两面概率相等硬币，丢100次，问连续4次正面的概率是多少？
Flipping 100 fair coins, how to calculate the probability that at least
one set of
continuous four heads happen in the 100 flipping sequence?
谢谢！ |
|
L*****e
发帖数: 169 | 39 flip a coin, p for heads, 1-p for tails, what is the probability
that the number of heads equal the number of tails, assuming infinite
number of flipping? |
|
c*******d
发帖数: 255 | 40 assume 2*N flips, and we'll let N->infty
the probability of having N heads and N tails is
Pr = C(2N, N)*p^N*(1-p)^N
= (2N)!/(N!)^2 *[p(1-p)]^N
using sterling formula, we have
Pr = [sqrt(2 pi 2N)*(2N/e)^(2N)*(1+O(1/N))] /
[sqrt(2 pi N) * (N/e)^N*(1+O(1/N))]^2 * [p(1-p)]^N
~= 1/sqrt(pi N) * [4p(1-p)]^N
since 4p(1-p) <= 1, we have [4p(1-p)]^N <=1
thus Pr -> 0 as N-> infty |
|
t*****e
发帖数: 53 | 41 This is an old problem. But I didn't figure out how to do it. So, 请大侠们
give a detail how to solve it, not just the answer.
Keep tossing one coin until either HHHT or HTHT shows up, What is the
probability of having HHHT
I am CS major, so, if you could provide some background material, thats
would be even more appreciated. |
|
z****i
发帖数: 406 | 42 don't know whether I'm thinking it correct...
the probability is the same as that of having HH before HT, which is just 1/
2.
don't know whether there is a general method for this kind of problems,
waiting for big niu... |
|
j*****4
发帖数: 292 | 43 The members of a company decide to give each other presents in the following
way. Everybody brings a present, which is put with the others,mixed and dis
tribued at random to the people. what's the probability that nobody gets his
own presents? |
|
i*****e
发帖数: 159 | 44 is there any better way to come up with E(Y) = 3 then simple induction like
E(Y) = 1/5+4/5*(1+1/4*1+3/4*(1+1/3*1+2/3*(1+1/2*1+1/2*(1+1))))?
If the two digits are "no repeats", the probabilities in your equation
should be 1/4 and 3/4? |
|
s********t
发帖数: 31 | 45 There are 10 red balls, 20 blue balls, and 30 green balls in a box.
You take them out one by one randomly.
Question:
What is the probability that when all red balls are taken out, there are
still at least 2 blue balls and 2 green balls in the box? |
|
s********t
发帖数: 31 | 46 The method in Zhou (usinng conditional probability) will work but the
process is a little complicated. For example, it is complicated if there
are at least 4 blue, 4 green balls before all red balls are taken?
Wonder if there is other method more elegant, e.g., using combinatorial
analysis? |
|
s******a
发帖数: 184 | 47 针对一个随机数据有一个已知的采样集，估算这个数据的probability distribution
一般用那些方法？ |
|
s******a
发帖数: 184 | 48 请问在R 或者 matlab 里怎么计算两个probability density 的covolution？ |
|
y**y
发帖数: 25 | 49 suppose you roll a dice twice consecutively,
what is the probability that the sum of the two numbers you got is 8. |
|
f*******s
发帖数: 57 | 50 Consider the strategy of picking number i with probability proportional to 1
/i, regardless of the counterparty's strategy, the expected payoff (for the
buyer) or cost (for the seller) is 1/(1+1/2+...+1/100), which is the price
that makes sure there is no-arbitrage, hence the fair value of the game. |
|
